1962 05_#21 05 #21

1962-05_#21 1962-05_%2321

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AMERICAN FEDERATION OF INFORMATION PROCESSING SOCIETIES

1962

PROCEEDINGS
SPRING JOINT COMPUTER CON FERENCE
SAN

FRANCISCO,

CALIFORNIA. MAY

1-3,

1962. VOL.

ADDITIONAL COPIES
Additional copies of the Proceedings maybe purchased
from the printer at $6.00 per copy and will be sent postpaid
if order is accompanied by remittance.
Orders should be sent to:
The National Press
850 Hansen Way
Palo Alto, California

DISCLAIMER
The ideas and opinions expressed herein are solely those of
the authors, and are not necessarily representative of, or
endorsed by, the 1962 Spring Joint Computer Conference
Committee or the American Federation of Information
Processing Societies.

Manufactured in the U.S.A. by The National Press, Palo Alto, California

PREFACE

This volume embodies the substance of technical presentations made
at the first of two major computer conferences to be held this year. Taking
a name which designates when it took place, rather than its geographic
location, the 1962 Spring Joint Computer Conference heralds recognition
that these meetings are nationwide in scope, no longer mere regional conventions. AFIPS continues the tradition of the former Western Joint Computer Conferences by bringing together from all parts of the country men
of talent who can provoke and inspire us to meet the challenges which
face our industry today.
Each paper presented has been selected for the unique contribution
which its author can make toward satisfying our industry's appetite for
new ideas. Rather than catering to anyone specific theme, this program
touches the highlights of new developments, points out trends, summarizes
progress, and orients the computer field with other disciplines.
We trust that this book will meet the need for which it was designed:
to serve as a valuable source of reference to a collection of technical literature for the computer industry.

G. A. Barnard, 3rd
Chairman
1962 Spring Joint Computer Conference
iii

AMERICAN FEDERATION OF INFORMATION PROCESSING SOCIETIES
AFIPS came into being as an unincorporated society of societies on May 10, 1961. AFIPS is a
direct outgrowth of the National Joint Computer Committee (NJCC). The latter organization was
formed in 1951 for the sole purpose of sponsoring and coordinating the Joint Computer Conferences, Eastern and Western. The same organizations which comprised the NJCC are the founding
societies of AFIPS:

The American Institute of Electrical Engineers (AlEE)
The Association for Computing Machinery (ACM)
The Institute of Radio Engineers (IRE)
Officers, Directors, and Committee Chairmen of AFIPS are:
CHAIRMAN GOVERNING BOARD: Dr. Willis H. Ware, The RAND Corporation, 1700 Main Street,
Santa Monica, California
EXECUTIVE DIRECTORS: R. A. Imm-AIEE; Dr. H. D. Huskey-ACM; Dr. A. A. Cohen-IRE
SECRETARY: Miss Margaret R. Fox, National Bureau of Standards, Data Processing Systems Div.,
Washington 25, D.C.
TREASURER: Frank E. Heart, Lincoln Laboratory, Room B-283, P.O. Box 73, Lexington 73, Massachusetts

AlEE DIRECTORS

ACM DIRECTORS

IRE DIRECTORS

R.A.lmm

Walter M. Carlson

Dr. Werner Buchholz
IBM Corporation
South Road Laboratory
Poughkeepsie, New York

IBM Corporation
Dept. 550, Bldg., 006-1
3605 Highway 52 North
Rochester, Minnesota

Mechanical Research Laboratory
E. I. duPont DeNemours & Co.
101 Beech Street
Wilmington 98, Delaware

Dr. Arnold A. Cohen
R. S. Gardner

American Institute of
Electrical Engineers
345 East 47th Street
New York 17, New York

Dr. Bruce Gilchrist
IBM Corporation
590 Madison Avenue
New York 22, New York
Dr. Harry D. Huskey

Claude A. R. Kagan
Western Electric Company
P.O. Box 900
Princeton, New Jersey

Dept. of Mathematics
University of California
Berkeley 4, California

517 Anthwyn Road
Merion Station, Pennsylvania

Frank E. Heart
Lincoln Laboratory, Room B-283
P.O. Box 73
Lexington 73, Massachusetts
Harry T. Larson

J. D. Madden
Dr. Morris Rubinoff

Remington Rand Univac
Univac Park
St. Paul 16, Minnesota

System Development
Corporation
2500 Colorado Avenue
Santa Monica, California
v

Aeronutronic, Division of
Ford Motor Company
P.O. Box 486
Newport Beach, California

AMERICAN FEDERATION OF INFORMATION PROCESSING SOCIETIES (Continued)
ADMISSIONS COMMITTEE

FINANCE COMMITTEE

PUBLICATIONS COMMITTEE

Dr. Bruce Gilchrist
IBM Corporation
590 Madison Avenue
New York 22, New York

Dr. Morton M. Astrahan

Dr. 'Verner Buchholz

IBM Research Laboratory
Monterey and Cottle Roads
San Jose 14, California

IBM Corporation
South Road Laboratory
Poughkeepsie, New York

AWARDS AND PRIZES
COMMITTEE
Claude A. R. Kagan
Western Electric Company
P.O. Box 900
Princeton, New Jersey
BY-LAWS AND
CONSTITUTION COMM..lTTEE

COMMITTEE ON
NEW ACTIVITIES
Dr. Morris Rubinoff
517 Anthwyn Road
Merion Station, Pennsylvania

SOCIAL IMPLICATIONS OF
INFORMATION PROCESSING
TECHNOLOGY COMMITTEE
Harry T. Larson
Aeronutronic, Division of
Ford Motor Company
P.O. Box 486
Newport Beach, California

Walter M. Carlson
Mechanical Research Laboratory
E. I. duPont deNemours & Co.
101 Beech Street
Wilmington 98, Delaware

PUBLIC RELATIONS
COMMITTEE

AFIPS REPRESENTATIVE
TO IFIPS

CONFERENCE COMMITTEE

J. D. Madden

I. L. Auerbach

Keith W. Uncapher
The RAND Corporation
1700 Main Street
Santa Monica, California

System Development
Corporation
2500 Colorado Avenue
Santa Monica, California

Auerbach Electronics
Corporation
1634 Arch Street
Philadelphia 3, Pennsylvania

1962 SPRING JOINT COMPUTER CONFERENCE COMMITTEE
CHAIRMAN: G. A. Barnard, Philco WDL, Palo Alto, Calif.
VICE CHAIRM..4.N: Dr. H. D. Crane, SRI, Menlo Park, Calif.
SECRETARY-TREASURER: R. A. Isaacs, Philco WDL, Palo Alto, Calif.
L. J. Borrego, Philco WDL, Palo Alto, Calif.

TECHNICAL PROGRAM

REGISTRATION

Chairman: Dr. R. I. Tanaka, Lockheed, Palo Alto, Calif.
Vice Chairman: R. C. Minnick, SRI, Menlo Park, Calif.
Assoc. Chairman: J. E. Sherman, Lockheed, Palo Alto,
Calif.

Chairman: D. E. Eliezer, IBM, San Jose, Calif.
Vice Chairman: Leo Rinsler, IBM, San Jose, Calif.
R. A. Shaw, IBM, San Jose, Calif.
PRINTING AND MAILING
Chairman: W. O. Hamlin, Fairchild, Mountain View,
Calif.
Vice Chairman: R. J. Johnston, Fairchild, Mountain
View, Calif.

SESSION CHAIRMEN:
F. M. Tonge, Stanford University, Calif.
R. A. Kirsch, Nat'l Bureau of Standards, Wash., D.C.
J. I. Raffel, Lincoln Laboratory, Lexington, Mass.
D. C. Engelbart, SRI, Menlo Park, Calif.
B. G. Farley, Lincoln Laboratory, Lexington, Mass.
J. H. Pomerene, IBM, Yorktown Heights, N.Y.
V. L. Larrowe, University of Michigan
Jack Goldberg, SRI, Menlo Park, Calif.
B. A. Galler, University of Michigan
Louis Fein, Consultant, Palo Alto, Calif.
H. K. Skramstad, Naval Ordnance Lab, Corona, Calif.
R. M. Bennett, IBM, San Jose, Calif.
J. P. Runyon, Bell Telephone Lab, Murray Hill, N.J.

PUBLICATIONS
Chairman: E. T. Lincoln, IBM, San Jose, Calif.
Vice Chairman: J. J. McNulty, IBM, San Jose, Calif.
PUBLIC RELATIONS
Chairman: N. S. Jones, Friden, San Leandro, Calif.
Vice Chairman: R. D. Painter, Fairchild, Mountain
View, Calif.
EXHIBITORS' PROGRAM
Chairman: D. C. Lincicome, SRI, Menlo Park, Calif.
LADIES' ACTIVITIES
Chairman: Margaret G. Conley, IBM, San Francisco,
Calif.
Vice Chairman: Anne Niemi, IBM, San Francisco, Calif.
Joy Gallagher, IBM, San Francisco, Calif.
Barbara Taylor, IBM, San Francisco, Calif.

EXHIBITS
Chairman: J. W. Ball, Pacific Telephone, Sacramento,
Calif.
Vice Chairman: Art Scholar; Pacific Telephone, San
Francisco, Calif.

SPECIAL EDUCATION PROGRAM
Chairman: R. J. Andrews, IBM, San Jose, Calif.
Vice Chairman: William Gerkin, Rem. Rand, San Francisco, Calif.
Bryce Ells, IBM, San Jose, Calif.
A. J. Bodine, IBM, San Jose, Calif.
E. W. Means, Rem. Rand, San Francisco, Calif.

LOCAL ARRANGEMENTS
Chairman: R. G. Glaser, McKinsey & Co., San Francisco, Calif.
Vice Chairman: R. D. Smith, Smith-Corona Marchant,
Oakland, Calif.
G. W. Mills, Burroughs, San Francisco, Calif.
H. G. Asmus, General Electric, Phoenix, Ariz.
D. C. Hays, General Electric, San Francisco, Calif.

CONSULTANTS
Exhibits: J. L. Whitlock Associates, Oakton, Va.
Public Relations: W. C. Estler, Palo Alto, Calif.
vii

REVIEWERS
AFIPS and the Conference sincerely appreciate the excellent job done by
the Reviewers. Their careful study and comments have been vital to maintaining the high standards of quality for this collection of papers.
S. Amarel
W. L. Anderson
M. M. Astrahan
D. C. Augustin
J. A. Baker
R. M. Barnett
R. C. Baron
D. E. Beecher
G. A. Bekey
R. M. Bennett
D. F. Berg
J. E. Bertram
E. Bloch
E. K. Blum
E. V. Bohn
A. Bridgman
W. Buchholz
T. H. Bullock
F. Carr
A. B. Clymer
M. Cohn
L. J. Craig
T. H. Crowley
E. C. DeLand
J. F. Dirac
C. B. Dowling
J. Earle
R. D. Elboum
G. F. Emch
D. C. Engelbart
G. W. Evans
B. G. Farley
I. Flores
S. Frankel
W. S. Fujitsubo
B. A. Galler
H. L. Gamer

R. A. Kudlich
V. L. Larrowe
R. S. Ledley
C. y, Lee
C. T. Leondes
B. M. Levin
M. H. Lewin
J. D. Little
B. Loveman
J. Lyman
O. L. MacSorley
J. Macy, Jr.
J. Mangnall
W. Marggraf
F. N. Marzocco
M. S. Mason
M. S. Mayzner
E. J. McCluskey
M. E. McCoy
R. M. Meade
R. Meagher
R. E. Miller
R. C. Minnick
M. Morgan
T. H. Mott, Jr.
P. G. Neumann
L. W. Neustadt
C. J. Nisson
H. Nonken
A. B. N ovikoff
M. Paskman
G. T. Paul
A. Pohm
J. H. Pomerene
C. R. Porter
T.F.Potts

J. P. Gibbons
B. Gilchrist
M. C. Gilliland
E. L. Glaser
R. C. Gold
E. A. Goldberg
J. Goldberg
M. H. Goldstein
E. Goto
G. R. Grado
D. Greenberg
J. Griffith
D. Haagens
D. W. Hagelbarger
J. K. Hawkins
L. D. Healy
P. J. Hermann
T. R. Herndon
T. Higgins
W. H. Highleyman
M. E. Homan
R. D. Horwitz
R. M. Howe
K. Iverson
A. S. Jackson
G. T. Jacobi
S. Jamison
D. B. Jordan
J. A. Joseph
L. Kanal
W. J. Karplus
W. Kindle
R. A. Kirsch
R. H. Kohr
G.A.Kom
L. D. Kovach

This list was compiled of all reviewers registered as of the date this book went to press.

J. I. Raffel
M. J. Relis
S. Rogers
H. Rosenberg
A. I. Rubin
M. Rubinoff
B. W. Rudin
J. P. Runyon
T. T. Sandel
C. M. Schoenberg
N. R. Scott
F. F. Sellers
W. L. Semon
N. Z. Shapiro
Q. W. Simkins
H. K. Skramstad
W. R. Slack
A. Slade
K. H. Speierman
R. I. Tanaka
H. M. Teager
D. Teichroew
L. E. Thibodeau
R. B. Thomas
R. M. Tillman
F. M. Tonge
K. B. Tuttle
G. Vandling
R. L. Van Hom
H. R. Van Zoeren
L. M. vVarshawsky
G. P. Weeg
R. R. Wheeler
H. K. Wild
R. O. Winder
C. H. Wolff

EXHIBITORS
This list was compiled as of the date this book went to press.
Aeronutronic Division of Ford Motor Co.
Newport Beach, Calif.

Consolidated Electrodynamics Corp.
Pasadena, Calif.

AMP, Inc.
Harrisburg, Penna.

Control Data Corp.
Minneapolis, Minn.

Ampex Corp.
Redwood City, Calif.

Datamation
New York, N.Y.
Data Products Corp.
Beverly Hills, Calif.

ANelex Corp.
Boston, Mass.

Datapulse, Inc.
Inglewood, Calif.

Applied Dynamics, Inc.
Ann Arbor, Mich.

DI/AN Controls, Inc.
Dorchester, Mass.

Automatic Electric Sales Corp.
Northlake, Ill.

Digital Equipment Corp.
Maynard, Mass.

Bell Telephone System, Pac. Tel. Co. and
Long Lines Dept.
San Francisco, Calif.

Digitronics Corp.
New York, N.Y.

The Bendix Corp., Bendix Computer Div.
Los Angeles, Calif.

DYMEC Div. of Hewlett-Packard Co.
Palo Alto, Calif.

Berkeley Div. of Beckman Instruments
Richmond, Calif.

Electro Instruments, Inc.
Sunnyvale, Calif.

Brush Instruments Div. of Clevite Corp.
Cleveland, Ohio

Electronic Associates, Inc.
Long Branch, N.J.

Bryant Computer Products
Walled Lake, Mich.

Electronic Engineering Co. of Calif.
Santa Ana, Calif.

The Bureau of National Affairs, Inc.
Washington, D.C.

Electronic Memories, Inc.
Los Angeles, Calif.

Burroughs Corp.
Detroit, Mich.

Engineered Electronics Co.
Santa Ana, Calif.

California Computer Products, Inc.
r!l Hf
-nnumP"
_ ..

Epsco, Inc.

C-E-I-R, Inc.
New York, N.Y.

Fabri-Tek, Inc.
Amery, Wis.

Collins Radio Co.
Dallas, Texas

Fairchild Semiconductor
Mountain View, Calif.

Comcor, Inc.
Denver, Colo.

Ferranti Electric, Inc.
Plainview, L.I., N.Y.

Computer Control Co., Inc.
Los Angeles, Calif.

Friden, Inc.
San Leandro, Calif.

Computer Systems, Inc.
Monmouth Junction, N.J.

Gen. Dynamics/Electronics Information Tech. Div.
San Diego, Calif.

--~.l'

""~~1..._!.l~~

~----'

~, and-E..~!f!r~-where-3.y.!y.!~ may form, will
be underlined. The description may begin as a
catalog of observations.
Books in the return bin are
In-the stacks-:-'-'-' -.-

In conducting this type of modeling:

~~~~~~

~2k~ from the r~~~ E..f~ are ~ by Yf~~~~~~

and placed in the
The basic modeling concepts are those of
activity, activity performer, transient information record, and queue. A caricature of the
system drawn upon these concepts places the system
in an information-processing context. Activities
may be defined as series of arithmetic-logical
operations--algorithms. Activity performers may
be identified by quantitative and logical descriptors, and transient information records contain
like descriptors by definition. Such a model is
relatable to the phenomena under study and conveniently translated to computer code.

r~1~ E..~~.

Yf~f~~~~ generate re3.u!s1s_f2r_b20~s
1h~ in the r~3.~~~1 E,~~.

and

place

H1>~~~~~~ examine re3.u~s1s_f2r_b20!S from
r~3.~~~1 E,~~ and place 1h~m in the !~~
E,~~.

the

9~E;:rf~ ~ r e,g,U!!S1s against :!?,o2k! in ~~!:~!~
and either ~ E,02k in !.~~~.E..~!! or ~
!e3.u~s1s in 2~1.E,~~.

A flow chart may be constructed at this point
which fixes the relationships of the components
thus far identified (see figure 1).

Potential queues are identified,

Transient information in the system is
identified,
Activities are separated from the people
or machines who perform them,

Thus far, the flow chart shows no control
activities, that is no activities directing the
flow of information, modifying queue disciplines,
or allocating performers among activities. A twodimensional flow chart is limited in application
to fairly stable component relationships. At same
point in modeling, the transient information flow

TOWARD A GENERAL SIMULATION CAPABILITY

chart becomes incapable of rendering component
relationships intelligibly, although flow charts
continue to be of value where relationships are
relatively stable; e. g., in the internal functions
of an activity.
The transient information flow chart must be
read as consisting of the routes of information
intersecting the processes performed upon the
information, and the buffers where the information
reposes when not being acted upon. The fact that
performance of a process is contingent upon allocation of activity performers and availability
of required information must be borne in mind. If
the routing of information is not fixed, the transient information flow chart may become burdened
with contingencies to the extent that its utility
disappears.
The following control activity might be one
added to the library model:

Hl>::lH'f*

aSSigns £l~.r!!.s to ~t~.ri~ E,o£k~ if

.9.~~ in_r~t:!:!I'!! E,i,!! is longer than .9.~~ in
~ !i,!!d_bin, or to !!!B-!c!!i~_r~<@e~t~ if
.9.u~u~ !n_f!n~ ~i,!! is longer than .9.u~u~ in

return bin.
----Note that here activities and activity performers, as well as queue content are treated as
transient information.
A number of additional control activities are
necessary to move the librarian from activity to
activity, get her and the clerks to work in the
morning, etc.
Each of the activities must be described by
an algorithm. The compOSition of the algorithm
will identify information exchanged with other
activities which must be contained in the records
passed between them. Information used in control
activities may be obtained from control blocks
associated with the various activities, activity
performers, and queues (buffers).
The modeling of a system with SIMPAC requires
the unambiguous statement of much information.
Consider the activity, "Generate requests for
books." How long does it take a viSitor to generate a request? Is this time constant or is there
a distribution of such times? Does each visitor
generate one request, or more?
The model of generation activity may include
sampling from Poisson, normal, or rectangular distributions for determining the number of requests
to generate during any time period, or the content
of any of the fields in the transient records
generated; e.g., what book.
Very likely the process will be stochastic,
but it need not be. The particular requests might
be input to the model as exogenous events, if so,
actual history might be utilized in defining these
events.
There are no simple rules for going about

this. Each of the activities is a highly aggregated representation of a portion of the system.
The completed model is a caricature of the system,
and each component of the model a caricaturistic
sum of myriad phenomena. Modeling serves to
clarify understanding of the system and indicate
areas of insufficient knowledge. It is the purpose of SIMPAC to provide building blocks for
expressing the model and a framework on which to
rest them.
Translation of the Model to COsPuter Code
Once a model has been specified in terms of
activities, performers, transient information records, and queues (or buffers), it is necessary to
translate the model to machine language--instructions and data.
SIMPAC provides, in the form of macro definitions, a simulation-oriented extension of the
normal symbolic instruction set. ExpreSSions for
entities like queues, and for operations upon them,
form this extension. For example, 'QTAKD A,B' is
an expression for: 'select a record from queue B
in accordance with the queue discipline found at
A'. 'GETBL A' for: 'secure a free block of storage from list A'. 'MCNRN A,B' for: 'generate a
sample drawn from a normal distribution, mean A,
standard deviation B'. 'X ACMAC A,B,C,D,E' for:
'there is an activity X, which services transient
information records in queue A, selecting them
according to the prevailing discipline found at B,
and requiring the expenditure of an amount of service time equal to C times the content of record
field D before placing the record in queue E'.
All activities are modeled as pairs of
algorithms: A set-up phase in which information
necessary for performance is gathered and a
resource time of performance computed, and a completion phase in which the activity itself is performed. The activity is considered "in process"
between the performance of set-up and completion,
and the time between is a function of activity
performer allocation.
Control Blocks.
has a control block.

Each component of the model

The activity control block contains:
The addresses of the set-up and completion
phases of the algorithm expressing the
activity.
Variables which indicate the performer
time necessary for the current performance
and the performer time thus far spent upon
performance.
A busy:not-busy indicator to show an inprocess state of the activity.
The minimum, maximum, and current performer allocations.

STUDY OF BUSINESS INFORMATION SYSTEMS

Counters of the number of times the activity has been performed, of the amount of
performer time expended upon performance,
and of the amount of performer time spent
on idle for lack of fulfillment of necessary conditions.

Each cycle the time increment is multiplied
by the performer allocation of the activity to
produce an amount of performer-time. Performertime is then applied to the activity, resulting in
partial or multiple performances, or accumulation
of idle performer-time.

The addresses of the activity's input and
output queues.

The computer code necessary to perform certain common operations is contained in a coherent
group of over sixty subroutines. The performance
of a given service may require the operation of
several subroutines.

The activity performer control block contains:
A count of currently available performers.
The unit of this count is a function of
their separability.
A count of the number of activities to
which these performers are assignable.
A list of assignable activities wherein a
block for each activity indicates its
activity control block address, the
address of an algorithm for determining
the effective value of assigned performers,
and the current allocation.
A count of performers assigned to 'other'
activities than those in the list.
Transient information records may represent
bearers of information or physical entities. The
record is made up of a number of logical fields
sufficient to identify the entity in the context
of the system. A particular format may serve for
many records, and occasionally the same record may
appear in several queues. The control block identifies the format of the record.
The queue control block indicates:
The current count of waiting records.
A list of these records.

An indication of the order

in which the

records are held.
The ordered mix of SIMPAC macro expressions
and symbolic expressions is merged with the body
of the SIMPAC program and compiled by a generalpurpose compiler. The program produced is the
SIMPAC program supplemented by the particular
model. See figure 2.
Moving the Model Through Time
The basic SIMPAC program contains modules for
effecting operations called out by various macro
expressions and routines which handle the
mechanics of moving the model through time and
recordir~ its performance.
The model is moved through time by a cycling
routine which steps each activity by a fixed increment of time. The inc,rement is variable from
one rlli~ to another, however, and the scheme is
adaptable to varying the increment from cycle to
cycle as a function of predicted events.

Each of the SIMPAC subroutines performs some
particular service in one of the following areas:
initialization and production of exogenous events;
clock and calendar timekeeping; delayed transmission of records; queue manipulation; associative
storage control; raw data recording; data analysis
and output presentation; distribution sampling;
miscellaneous, including table-look-up, square
root, etc.
Familiarity with the routines is not required
of the user, merely familiarity with the macro
instructions and their usage.
(Each subroutine in the SIMPAC program is
consistent with conventions of modularity so that
portions of the program, and the associated macro
expressions, may be useful in the implementation
of information-processing systems unrelated to
simulation: e.g., the associative storage
mechanisms.
It is conceivable that the simulation of a
planned information-processing system might result
in the development in the model of activity algori thms directly transferable to the actual system.)
SIMPAC Associative Storage. The queue control block contains the addresses of the first and
last queue words, each of which contains a referent address of a transient record and the
address of the following queue word. Records
contain no link to other records in the same
queue. This indirect catenation permits multiple
concatenations of records without incurring redundancy of the information contained and avoids the
physical movement of records (see figure 3).
Queue words are each one word of computer
storage. Transient information records vary in
length with the number and size of logical fields
contained and are conjunctive.
SIMPAC contains a device to enable the sharing of available storage by queue words and
transaction records, thus eliminating arbitrary
limits upon queue lengths. The device is as
follCtllS:

An initial associative allocation of 1, 2,
3, ... n word blocks is made to push-dmm/
pop-up lists; n is a multiple of all
smaller blocks, and most available stor~~e
is allocated to n word blocks.

TOWARD A GENERAL SI\1ULATION CAPABILITY

Free blocks are made available and returned by macro instructions.
Automatic communication with a storage
banker routine is established "'Then a control word of a push-down/pop-up list
indicates no more blocks are available.
The storage banker diverts n word blocks
to 1, 2, 3, ... word blocks as needed, or,
in a second mode (when n word blocks are
exhausted) builds larger blocks from
available conjunctive smaller blocks.
This operation consumes little computer time
(with the exception of mode 2 of the storage
banker which involves tape movement) and provides
great flexibility of storage utilization.
Although records in a queue are not conjunctive, they are recorded on tape as a continuous
record.

This is a fairly general flworld view" and, as
a result, SIMPAC is a fairly general simulation
tool.
Muse is the name given to the project of
developing a simulation capability more general
and more efficient than SIMPAC. The name is appropriate in that simulation is a blend of art and
science, and several - if not nine - simulation
systems may be developed. These systems will be
developed with more regard for pure theoretical
considerations than was SIMPAC, whose development
was greatly influenced by immediate, practical
considerations. This is not to say that practical
considerations will be ignored; they will be
weighed, but the practical considerations will be
tomorrow's rather than today's.
Before introducing the special II world Vie1-1"
upon which Muse is based, several terms which have
been used throughout this paper are defined.
'Model' - 'A representation of an aggregate
of phenomena'

Output Presentation

'Symbol' - 'A representation of a phenomenon'

Before a simulation run is made, data recording parameters are fixed, which determine the raw
data which will be recorded as the model is moved
through time.
Available outputs are limited by the fund of
raw data made available by the recording routines.
The data which may be recorded are the content of
the three control blocks (queue, performer, and
activity) and the content of the transient records
in the queues.
After the simulation run, output listings are
produced in accordance with list requests phrased
with a small vocabulary of macro expressions. The
output phase of the program may be rerun as often
as desired, producing whatever listings might be
of interest.
Sample listings are shown in figure 4. 1 Time
series listings of selected variables, functions
of the series, and, as in the case of the listings
illustrated the particular contents of queues the discrete records, or summaries of the contents,
may be obtained.
Part 3: Muse

SIMPAC is prea1cated upon a Weltansicht which
recognizes systems as complexes of transient information, queues formed in the system's buffers
by transient information records, algorithms which
generate, use and destroy this information, and
performers of these algorithms.

~rom tests of
Mark I model.
put phase (SDC
Calif.: System
1961. 18 pp.

the Management Control Systems
See Patricia McKeever, SIMPAC outdocument FN-5256). Santa Monica,
Development Corporation, April 20,

'Simulation' -

'~JUamic representation of
dynamic phenomena'

'System' - 'A body of phenomena'
'Object system' - 'A system to be modeled;
the system under study'
A symbol is a representation of a unity, a
whole. A model is a representation of an entirety,
an aggregate whole. A sLuulation model is a
representation in time of an aggregate whole, a
representation of a dynamic, aggregate whole.
Mere aggregations of phenomena need not be systems
but may be modeled. An aggregation of phenomena
is a system if it forms an organic whole.
Weltansicht: there are things, and every
thing may be from time to time, in several logical
states. A logical situation is a particular
pattern of certain things in certain states. Multiple occurrences of similar things in similar
states may give rise to multiple occurrences of
similar logical patterns and thus multiplicities
of similar logical situations. Certain logical
situations invite the exertion of forces which
affect those things in the logical si t.uat.iorI,s;
destroying the situations. Thus things are
created, destroyed, and placed in different states.
this

The following definitions are adopted from
II wor ld view. II
'Logical situation' - 'A logical pattern
formed of certain things in certain
states'
'Total logical situation' - 'The logical
pattern formed of all things'
'Event' - 'A change in a logical situation'

STUDY OF BUSINESS INFORMATION SYSTEMS

1.3 FYlQ

'tvenement' - 'A change in total logical
situation'

=¢

QrlT = ¢
1.5 T()F s¢

1.4
'Unstable logical situation' - 'A l.s. which
invites the exertion of a force'
'Stable logical situation' - 'A l.s. which
does not invite the exertion of a
force'

1. 6

This definition of 'evenement,l does not
admit of simultaneous evenements. There may be
simultaneous events, but they produce but one
change in total logical situation.

1.7

'Q' - 'The class of logical situations'

Several simulation systems will be developed,
based upon these concepts. In all models constructed within these systems, things and thing/
states are represented by symbols, forces are
represented by algorithms, and logical situations
are represented by patterns of thing/state
symbols.

2'-

A thing is, or it is not.

cp~X

Explanation: The number of forces corresponds to the number of unstable total
logical situations and the number of
possible evenements, at most equal to
the number of total logical situations.

'F' - 'The class of forces'

'T' - 'The class of things'

Explanation:

Abbreviation:

For 'object system nt, IO,S'n'

An object system must be stated in simple
terms in Sl, due to 1.6.
Example.

In 0.8'1 there are 4 things, and 3

unstable logical situations.

(Recall there are no

thing/states in Sl.)

X = 16

1.6

A loose description of the first, and basic
system follows. The system, Sl, is predicated on
a simplified interpretation of the Weltansicht,
and is inchoate at this writing.

A number from a to 15 may be assigned to each
possible logical situation; thus:

Sl does not contemplate thing/states, only
things. Furthenmore, multiple occurrences of
similar things are precluded. A thing is, or is
not.

There are 3 unstable logical Situations, and
so three forces:

In later systems, multiple occurrences,
thing/states, and individual characteristics of
similar things will be contemplated.
In Sl, the following rules and definitions
hold for any object system.

1.0

= ff l ,

f 2 , f3, ••• ,f~)

= r~,

= ff l ,

ql,···,q15 J

f2' f3}

Since the antecedent (unstable) and consequent (stable or unstable) logical situation for
each fi completely define each f , it is conveni
of

""""+ +,...

... - .........'"

of,:l 0 .... + of of',. of'
... ""' ................. J

of'
-1' -2'

of'
~.T"I +'h ,...., ..... .,. ... "1 r>
.."'" -3
..
..--..-.... -

0"",:1
~

c:",'h_
~~~-

cripts identical to their respective antecedent
and consequent logical Situations; thus:

'~' - 'the number of forces; the
cardinal of F'

1.1

Q = (ql' ~, q3""'~}

'X' - 'the possible number of total
logical Situations; the cardinal of
Q'
1.2

= (tl ,

t 2 , t3, ••• ,tTl

'the number of thingsj the
cardinal of T'
ITI

Inspection of this statement of F makes
possible identification of a set of sequences of
total logical Situations, or states, of O,S'l'

{(l, 3, 8), (4, 6)}
It is clear that if O,S'l is ever in state 1
it will proceed to state

state other than 1, 3, or

~'Evenement"

French for 'event', is used to
connote something more comprehensive than an
event.

8 and remain there; and

it is equally clear that if O,S'l is ever in a

4, it will remain there.

Sl, upon examination, is a very simple system,
AnalYSis of an object system is an almost trivial
task.

TOWARD A GENERAL SIMULATION CAPABILITY

This simplicity is its virtue. For if more
sophisticated systems (Sn) are developed whose
statement may be transformed to Sl statement, the
problem of system analysis will be greatly simplified. Algori tbms can be programmed which perform
model analysis.
The eventual scheme of operation might be as
follows:
1.

Statements concerning O,S'i in Sn.
modeler.

By a

Synthesis of a model of O,S'i in Sn.

Transformation of the Sn model to an Sl
model.

Analysis of the Sl model.

Translation of the Sl model analysis to
statements about the Sn model.

Presentation of the analysis to the
modeler.

7. Possible revision of the Sn model and
repetition of steps 1 through 6.
8.

Simulation runs of the Sn model.

Presentation of simulation results to the
modeler.

Figure 5 is an example of what a simulation
model in S2 or S3 might look like. upon transformation to Sl, ambiguities and inconsistencies
in such a model become identifiable. The possible
terminal states, as functions of initial states,
may be deducible.
Within the syntax exe~lified in figure 5,
quite co~lex statements may be written. These
statements may refer to individual characteristics
of things, states, and logical situations. For
example, duration time may be determined by a
formula containing occurrences of variables which
are functions of individual characteristics of
things occurring in the antecedent logical situation formula.
Summary. Muse is intended to provide a
system of analysis, modeling, and simulation which
will reserve to the student of systems the functions he alone may fulfill and which will delegate
as much as possible to machine. By delegating
deduction to machines and reserving premise and
hypothesis statement to humans, we expect to be
able to study the simulated behavior of very large,
very complex systems.

I-'

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Exogenous
Events

New or Changed
Model Components,
Cycler and
Recording Controls

Output
Requests

r::

Initializatio

Simulation

Data Analysis

Time
Series
and
Functions

OPERATION OF THE SIMPAC FROGRAM
FIGURE 2

~
~

.....

t-o

:First
Count

Discipline

,,'"

Last

.,~

Queue Control Block

en
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c::

t:l
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SIMPAC Associative Storage

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TOWARD A GENERAL SIMULATION CAPABILITY

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REFERENCE

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52f ... ,Yk), the magnitude
is defined by /'YI = (Y1 2 + y22 +... + Yk 2}1/2.
Norm. A measure which is not strictly the
vector magnitude as defined above, but is ordinarily easier to calculate. In the case of vector

== l'il

(Yl' Y2"'" Yk) the norm is defined by {V}
/Yk\' In any case, 1~ {YV/yI~k1

+ IY2 1 +... +

Unitize. To change the magnitude of a
vector to unity without changing the ratios of
components. If vector magnitude is used for
this purpose, the unitized components are defined by ~ == Yu/
If the vector norm is
used, the unitized components are defined by

IYI.

Yu=Y u

={y}.

Some Methods of Nonlinear Programming
With the help of the foregoing nomenclature, we
are in a position to describe some methods used
in nonlinear programming. Allusions to some of
these techniques are already in the literature
of optimization, and useful bases for the development of general nonlinear methods have long been
available. However, only two basic methods
have been developed sufficiently for wide use
in systems that have nonlinear constraints as well
as nonlinear objective functions.
In order not to lengthen this paper, we offer only
a brief description of these methods. The literature references should be useful to those desiring more information about particular techniques.

Analytical Method
Use elementary calculus and algebra to determine all proper maxima possessed by the objective function. The highest of these maxima
may be the solution, if feasible. Next determine
constrained local maxima subject to each of the
constraints and bounds (Lagrange's method of indeterminate multipliers is convenient for this).
The highest of these may be the solution, if
feasible and not surpassed in the earlier calculations. Next, do the same for local maxima
subject to pairs of constraints or bounds. Note
that there are (2K + q). (2K + q-l)/2 such pairs.
Continue in this way until all local maxima on
groups of constraints or bounds have been isolated. Then select the .global maximum. Some of
the mathematics required in this method may be
found in the literature. 9, 11
Grid Method
Space Yu values at reasonable intervals for each
variable (e. g., divide the entire range of each
variable into ten parts). Calculate F at each
feasible member of the (j1 + 1) (j2 + 1) ... (jk + I)
resulting grid points (where ju is the number of
intervals for variable yu)' Designate the point
with the highe st F value as the "fir st solution. "
If more precision is required, explore the vicinity of the first solution on a finer mesh than
before (or else apply some interpolation device,
such as a second-degree I!hypersurface"). Continue this until satisfactory precision is obtained.
Check the solution by making gradient or gradient-projection excursions. To reduce computing
time when using this method, eliminate protions
of the grid whenever possible by considering
analytical properties of the constraints. This is
sometimes called the "case study" method in
design work.
Monte Carlo Methods
Use a random number table (or generator) to
select a point in the bounded region. Retain this
point if feasible, and calculate its F. Repeat for
another random point. Retain the new point if
its F is higher than that of the old point. Continue in this way for a predetermined number of
points (calculated from statistical considerations
to give a preset confidence level). The last retained point is taken as an approximate solution.
Check this solution by making gradient or gradient-projection excur sions.
A variation of this method use s the retained
point as a start for the next move. Then the
direction of the move is determined at random,
but the magnitude is fixed. If a certain number
of moves does not produce an improvement, the
magnitude of the move is decreased. Brooks2

discusses some of the possibilities of these
methods.
Cross-Section or Univariate Method
With fixed starting values of Y2' Y3"'" YR'
vary Yl by preselected steps, spanning its range.
At each point, calculate F if feasible. Select the
best F so far and set the corresponding value of
YI' Then vary Y2 in the same way, and set Y2
according to the best feasible point so far. Continue in this way until a complete cycle produce s
no further change in F. As with the grid method,
a finer mesh may be introduced after the final
approximation is achieved. As usual, the solution must be checked by making eradient or
gradient-projection excur sions.
Blocking Methods
Consider the pos sibility of reducing the region
to be examined, in a systematic rather than a
random manner (d. Monte Carlo Methods). The
general idea is to eliminate about half of the
bounded region of coordinate space at each step.
These methods may be satisfactory for a small
number of variables, but they become unmanageable for a large number of variables because the
procedure requires a knowledge of the objective
function and of the constraint functions for at
least the "corners" of the region to be eliminated.
In a region with k major variables, there are 2k
such corners. For k = 20, this number is more
than one million.
Gradient Projection Method
From a feasible starting point, follow the gradient until stopped by a constraint. Follow this
constraint, via gradient projections on tangent
hyperplanes, until stopped by another constraint.
Then follow the two constraints, via gradient
projections on intersections of tangent hyperplanes, until stopped by a constraint. Follow
this constraint, via gradient projections on tangent hyperplanes, until stopped by another constraint. Continue in this way until "cornered"
(at a constrained maximum) or stopped by a zero
gradient or gradient projection (at a proper maximum or partially constrained maximum). Check
the final calculated point to see whether it is a
solution. Due to the use of tangents to approximate constraints, it will sometimes be necessary
to return to the feasible region when a calculated
step has led to a nonfeasible point. This is done
by an interpolation procedure. 8
Probe Methods
With preselected step sizes for all variables,
make excursions from a feasible point, in directions of increasing and decreasing Yu' The first
successful excursion (feasible point with improved F) determines the next point on the course,

STUDY OF BUSINESS INFORMATION SYSTEMS

and this point becomes a nucleus for further
probing. Continue the course until no improved
feasible point is achieved, due perhaps to approaching a constraint. A technique for following constraints is described in the section on
Subprogram EDGE, later in this paper.' When
a course terminates away from all bounds and
constraints, a nearby solution is indicated.
When the appropriate procedures have failed to
produce any advance, it is time to decrease the
step size and repeat the entire procedure. Mter
repeated reductions, the step size falls below
some tolerance, and the calculation stops, indicating a solution. The calculated solution is to
be checked via gradient or gradient-projection
calculations, provided that it is possible and
practical to calculate derivatives of the objective
and constraint functions.
A number of practical variations of the method
just outlined are possible. One of these involves
resetting the probe point to a bound whenever
such a bound is crossed in probing. Another
involves persisting with probes in a favorable
direction, once such a direction is established.
Another consists in designating certain variables
as "discrete, It in which case their increments
will be integer multiples of specified values
(usually unity), and the variables themselves
will take on only specified values {usually
integers}.
Figure 1 illustrates the general operations involved in a Probe program. The details are
discussed later.
Other Methods
Of course we should not, and do not, claim that
all methods of nonlinear programming have been
included in this summary. However, some
published methods l5 , 17 are so closely related
to linear programming that it is better to treat
them in publications on that subject. Other
methods 16 relate more specifically to special
classes of problems, for which the ultimate
solution depends on such methods as we have
already considered.
Comparisons. Experience with actual
programming and problem solving, using the
methods described above, has indicated that
either the Gradient Projection method or the
Probe method, or special combinations of these,
will prove most effective in attacking optimization problems which relate to evaluation, design,
or control of large systems.
Note at this point that, although some analogie s
do exist between Gradient methods and Probe
methods, essential differences also exist. For

A ~ONLINEAR DIGITAL OPTIMIZING PROGRAM FOR PROCESS CO:'lJ'TROL SYSTEMS

example, if the calculation of a derivative is not
possible or practical, the Gradient Projection
method cannot be used. On the other hand, if a
situation arises which demands only the most
rapid feasible advance, the Probe method is
ruled out.
Analytical procedures are rejected because of
the complications which would be encountered in
the usual control problem. Grid methods require
examination of too many !!cases!!; e. g., a rnillion
cases might be examined in solving a three-variable problem with a solution tolerance of 1% of
the range. Blocking methods are similarly
cumbersome. Monte Carlo methods may be useful for finding a solution, but in the usual form
they do not give information about the nature of
conditions close to the solution: such conditions
may be of considerable interest in a control
problem. Cross-section methods and variations
of Gradient Projection, now under study by
others, 8, 12 may be found to be interchangeable
with the methods that we have stressed.
In this paper, details of structure and program
are presented for Probe methods only.
Optimizing Subprograms
In the preceding section, general features of
Probe techniques were outlined. We shall now
describe in detail the principal subroutines which
are incorporated in the final program to be considered later. This program is simple in concept and application, but gives indication of being
suitable for use with large and complicated problems. In the sections that follow, the entire
program will be elaborated in enough detail to
guide coding for a stored-program computer.
Subprogram PROBE, shown in flow form in Figure 2, contains the basic logic of the "probe"
and is operative as long as special local conditions (e. g., regions where the gradient changes
sharply within one step, or regions near constraints) do not intervene. The basic procedure
is as follows:

with a fixed step size, this operation is under the
control of Subprogram ORDER. But if the return
to Subprogram PROBE from RIDGE or EDGE
shows no improvement, it is time to halve the
step size. When the step size falls below some
preassigned tolerance, the calculation will be
halted under direction of the main program.
In Figure 3, which shows a simple two-dimensional (schematic) problem with two constraints, thi::> subprogram is illustrated by the
course SABDEF. Note that for this course the
preferred direction is changed at B (under control of Subprogram ORDER), where it is not
necessary to go into Subprogram EDGE; and
again at F, where it is necessary to go into
EDGE.
The use of a flag, Key 23, for this branching, is
illustrated in Figure 2. Another function of
Subprogram PROBE is to select the critical
points (high and low feasible and nonfeasible
alternates) to be used in Subprograms RIDGE
and EDGE if needed.
Subprogram RIDGE, shown in flow form in Figure 4, is designed to maintain progre s s with
large steps even in regions where the gradient
changes sharply within one step. Suppose that
probes from the nucleus (at full step size) have
failed to indicate an impending constraint, yet
have also failed to yield an improved point.
Then before reducing the step size, proceed
as follows: between the two highest-valued probe
points, evaluate the midpoint. Break out of the
subprogram if the midpoint is nonfeasible
(failure) or if it is feasible and higher than the
nucleus (success). Otherwise, use the evaluation toge'ther with a quadratic approximation to
estimate the maximum F between the critical
probe points. The equations for this estimate
are:
Y IR = (I - r) y IA

+ ry IB

y 2R = (I - r) y 2A + ry 2B
r = (FA - F B) /2 (2FM - FA - F B)'

With preselected step-sizes for all variables,
probe, in a preset order, from a feasible point
(nucleus) in the (positive and negative) directions
of the basic variables. Desist as soon as a higher-valued feasible point is found; use this point
as a new nucleus. When the probes on all variables fail to produce an improvement, go into
Subprogram RIDGE, unless some probe point
was nonfeasible; in that case go into Subprogram
EDGE. Subprograms RIDGE and EDGE are discus sed later.
If progress is made for several (e. g., 4) steps

Here y I and Y2 repre sent the variable s involved
in probes that produce the highest feasible point
(A) and the next-highest feasible point (B); F is
the objective function; M represents the midpoint
between A and B; and r is a parameter used in
calculating the approximate maximum or "ridge"
point between A and B. This calculation is in
part based on a quadratic approximation of the
objective function on the ridge.
Figure 5 illustrates a course in which Subprogram
RIDGE is effective in using the midpoint for

20
several steps (SCFJ), then fails at the midpoint
(N) but succeeds at the quadratic approximation
(P).

Subprograni EDGE, shown in flow form in Figure
6, directs procedure after a constraint (or a
confluence of constraints) is sensed (Key 23 = 3).
It directs the course of computation so as to
"follow" the "nearest" constraint, unless improvement can be made in a direction away from
the constraint. An outline of procedure follows.
Since at least one of the probe points is nonfeasible and all probe points one step-size away have
been evaluated (otherwise we would not be in
EDGE), information is available to classify
highest-valued and lowest-valued feasible and
nonfeasible points. The classification may be
represented as follows:
Nonfeasible
Feasible
HN
Highest
HF
LF
LN
Lowest
Now, first test the midpoint between HF and HN.
If feasible, evaluate. If not better than the
nucleus, replace HF by the new point. Then
proceed similarly with LF and LN. Repeat the
procedure using HF and HN, as well as the procedure using LF and LN, at least four times before concluding that a revised choice of critical
points is required. Then combine the first- and
second-choice points according to the schedule
shown at the upper right in Figure 6, under control of flag K3. As usual, break out of the subprogram as soon as a point better than the nucleus is discovered.
In Figure 3, the combined use of Subprograms
PROBE and EDGE is illustrated by the course
FKLPWX. In this schematic example, the need
fur ::;tep-:;;iz.e reductiun due::. nut uccur until the
last step (which also involves resetting to a
bound).
For a single nearly linear constraint, as in the
diagram at the right of Figure 6, this procedure
must produce a point (such as L or H) which is
better than the nucleus and feasible, provided
that the value function is also nearly linear and
that we are not already at the optimum. (As a
matter of theoretical interest, this statement can
be proved for a number of variables and for more
general conditions than those implied here. )
Although these conditions may seem very restrictive, they commonly occur in practice, with
the result that Subprogram EDGE is very useful.
The approximation to linearity, of course, improves at sma11 step-size.
Subprogram ORDER, shown in flow form in

STUDY OF BUSINESS INFORMATION SYSTEMS

Figure 7, reorders the probe array JORD and the
constraint-calculating order array JCON when
needed in the interests of efficiency. The procedure used in probing is to bring the successful probe to the head of the list, and to remo"~"e
its complement to the end. For example, if the
probe order has been-3, +2, +1, -1, -2, +3,
and a successful probe is made on the fourth
trial (-I), the new probe order becomes -1, -3,
+2, -2, + 3, + 1. The array JCON is adjusted
according to a tally of the number of times that
individual constraints have been calculated negative during the course of a major cycle. The
largest frequency NC(K) determines the first
C(K) to be calculated in sequence, the next largest
NC(K) determines the next C(K}, and so on. This
eliminates superfluous calculations of constraints
likely to be positive, when a negative one is
sought. For a feasible point, the complete set
of constraints must be calculated in any case;
then the order is unimportant and will be left
unchanged.
Main Probe Program and Subroutines
The main program is shown in flow form in Figure 8. In addition to connecting the subprograms
and doing the necessary initializing, finalizing,
and branching, the main program also calls the
subroutines which define the problem. Such subroutines are defined in the following paragraphs.
General restrictions on formulation of problems
are also presented following the description of
the subprograms.
Problem Subroutines. The subroutines
that define the problem are briefly described as
follows:
1. ENTER. The optimization program will call
ENTER only at the start of the calculation. Accurdingly, Lhi::; ::;uuruuiine ::;huuld include all the
one-time operations required to set up the calculation. It will set the values of KY, Y, YL,
YH, and KC, normally by means of a data-load.
It may set an initial value for STEP, and values
for STEND and D. Although these are not essential (being calculable as fixed fractions of the
ranges of variables), a proper selection may
shorten the program running time. If discrete
variables are to be used, ENTER must set the
MQD values accordingly. ENTER can also be
used to load other data or parameters, perform
initial calculations, or provide an initial
printout.
2. SAVE. This subroutine is the fir st one called by the optimization program after it changes
the Y(I) values. To eliminate duplicate programs, calculations should be included here that
are common to several constraint functions, or

A NONLINEAR DIGITAL OPTIMIZING PROGRAM FOR PROCESS CONTROL SYSTEMS

common to the objective function and to some
constraint functions. Calculations which pertain
to the objective function alone, or to only one or
two constraint functions, ordinarily are omitted
from SAVE.
3. OBJECT. This subroutine sets VAL equal
to the value of the objective function at the specified set of Y(I). The subroutine can as sume that
SAVE results are consistent with the assigned
Y(I)' s, but must not use any results from FENCE,
since they may be inconsistent. Results reported
as VAL at successive points should represent a
single-valued function of the variables, and
should not vary randomly because of convergence
and roundoff errors. If such variations occur
in the last few digits of a calculated objective
function, they should be dropped before reporting
the value as VAL.
4. FENCE. This subroutine must set C(JC)
equal to the value of the constraint function for
the stored index JC, at the specified set of Y(I).
The subroutine can assume that SAVE results
are consistent with the assigned Y(I)' s, but must
not use any results from OBJECT, nor those
from FENCE for any other value of JC.
5. FOUL. If all C(I) values are positive or zero
at the initial set of Y(I) values, this subroutine
will not be used. However, if any C(I) is negative
at the start, it is recognized as nonfeasible.
The optimization program will attempt to find
a feasible start, without regard to the objective
function. After each unsuccessful try, it will
call FOUL. If the programmer wishes to follow
the results of these trials, he can program FOUL
to print out pertinent re suIts calculated by SAVE
and FENCE. Once a feasible point is reached,
OBJECT will be called. Thereafter, nonfeasible
points are treated as intermediate results with
no special provision for publishing. If the optimization program concludes without finding a
feasible point, it will set KERR = -1 and call
FINISH to terminate the calculations.
6. FAIR. This subroutine is called each time
a ne"\T/ nucleus is established. Thus the program=
mer can use FAIR to publish results of interest
for moves (points along the path to the optimum).
When de sired, FAIR can include machine options
to bypass the publication. Moreover, a short
testing routine at the start of FAIR can limit the
points published to insure that each published
VAL exceeds the previously published VAL by
some specified increment. Since FAIR may be
called several hundred times in a typical optimization, some limitation on either the points
published or the length of publication per point
is desirable.

In some calculations, the desired optimum may
actually be set in advance. For example, in
using an optimization technique to solve simultaneous nonlinear equations, the objective
function starts as a large negative number and
gradually approaches zero. In such calculations,
the programmer may wish to conclude the run
as soon as VAL approaches the known optimum
closely enough.

7. FINISH. This subroutine is called at the
conclusion of the optimization, for any of the
following reasons:
a. The optimization program or one of its subroutines declares an answer;
b. an error is indicated;
c. no feasible start is found; or
d. the machine is required for another problem.
The programmer
final calculations
detailed results.
be used to switch
FINISH.

can use FINISH to perform any
at the optimum and to publish
If desired, the error flag can
to a diagnostic routine within

General Restrictions. The programmer
should keep in mind the following restrictions.
1. The objective function, all constraint functions' and any intermediate variables used in
their calculations should be single-valued, real,
and calculable for any set of Y's with YL(I) ~ Y(I)
~YH(I) for all 1.
Discontinuous functions are not
ruled out, but should be subject to careful scrutiny during the course of the calculation. In some
case s it will be advisable to introduce an arbitrary function for the slope of a, discontinuous
variable, or to provide arbitrary (negative)
values for constraint functions and an arbitrary
(large negative) value for the objective function
at the discontinuity.

2. The subroutines must provide easy access to
the values of Y, YL, YH, C, KY, KC, JC, VAL,
KERR, STEP,STEND, D, MQD. (In FORTRAN
coding, this can be done by carrying these in the
+!_.-.+

rr\7.,K'?tJfr\1\T

,....1..-..1.. _ _ _ _ _ "'-

-L.L.1. O\..

V\.../.lVJ.J.V.l\...l.i.'1

OI,a.L..Cl..llt=:l.lL..

3. Subroutines SAVE, OBJECT, FENCE, FOUL,
and FAIR must not alter any of the above listed
values, except that OBJECT must set VAL,
FENCE must set C(JC), and any subroutine may
set KERR to an appropriate value if an error is
detected.
4. Adequate permanent storage must be provided for all of the above quanti tie s so that they are
always present, even though the subroutines may
be moved about or altered. (In FORTRAN coding,

22
this can be achieved with suitable COMMON and
DIMENSION statements. )
5. Limitations of the Probe Method. As indicated before, this Probe method does not pm"port
to be a "univer sal" optimizer, although it has
important advantages. As is true of all optimization programs known to the author, it is possible
to construct problems which will defeat the program. It is even expected that such problems
will arise in a practical setting, although none
such has yet come to our attention. For this
reason, a careful examination of calculated results is always required, from a mathematical
as well as an engineering standpoint.
In case the result obtained is a local maximum
and not a global maximum, even the careful
terminal examination is of no avail. As Rosen 8
indicates, no better way of achieving the global
maximum is yet known than that of proceeding
from several different starting points. These
starting points may be selected by a Monte Carlo
procedure, or by more rational means if the
problem is familiar to the programmer.
We note that there may be "pathological" features
of value functions and constraint functions capable
of defeating optimizer s. Analysis of such
feature s is outside the scope of this report.
They are generally associated with discontinuities
in derivatives of the value function or constraint
functions. These give rise to "essential nonlinearities" which render the reduction of stepsize futile as a mode of escaping from an unsatisfactory point in the calculation. An important exception is the case of a discrete independent variable; even though such a variable
introduces essential nonlinearities, it does not
defeat the Probe method.

STUDY OF BUSINESS INFORMATION SYSTEMS

not test for a global maximum but only for a local
maximum. In a problem which cannot be solved
analytically, the probability of achieving a global
optimum might be increased by solving the problem a number of times, using a different starting point each time.
A satisfactory criterion of "efficient" solution is
not so easily established. However, in order
to have some kind of indication, we suggest that
a solution be judged inefficient, if, in the cour se
of it, some constraint, or the objective function,
is calculated more than n e = k S log2 R max times,
where 15 is the number of major variables, Ru is
the range of a basic variable divided by the final
tolerance on that variable and Rmax is the greatest of the Ru'
Study of Tables 1, 2, and 3 sho,",vs that the pro~
gram achieved "successful" solutions of each
problem. Except in two extreme cases (B-2 and
B-3), the method is "efficient" by our criterion
(with s = 3, an arbitrary but probably reasonable
value). Of course, these results are merely
illustrative of the possibilities of the PROBE
program. Peculiarities of a given problem,
selection of a starting point, and choice of initial
step sizes and final tolerances may alter the
efficiency even on the same problem. Nevertheless, the PROBE program has performed well on
a wide variety of nonlinear problems, including
a "refinery simulationt! with ten variable sand
seventeen constraints 10. Therefore, this method
is recommended for further application to nonlinear problems (including control problems),
especially when complicated nonlinear constraints
are present.

6. Examples and Criteria for Numerical Testing.
Problems of different degrees of complexity have
been used to test the Probe program. The list
includes synthetic test problems, practical design problems, and the solution of algebraic
systems (simultaneous equations, curve fitting,
and rational approximation).
For the pre sent report, three te st problems are
selected and tabulated (Tables 1, 2, and 3) merely
to give the reader some indication of the relations
between problem data and program parameters.
A satisfactory criterion of "successful" solution
is easily established. The criterion (as suggested
earlier) is as follows: Within the preset tolerance, an excur sion along the gradient or gradient
projection should produce no better solution than
that already obtained. This, of course, does

Summary of Problem A

O~Yi~3(i=l,

l, 3,4)

C 1 = 3-YI-Y2-Y3-Y4~ 0

Test,

Starting
Values
Fo ! (0

i
Ye

Solution
Fe
I

!EfrtcienCY i
Criterion Tallies
R I ne ! ne1 nf

A-l

0.50
0.50
0.50
0.50

3.125

0.10
0.10
0.10
0.10

0.6586
1.6703
0.0000
0.0000

5.433 10.00211500
i 0 • 002 I l500

A-2

0.5?

3.750

0.10

?~5~
.. ov7v,.,l

5.433

, "

0.0000
0.0000

0.6586
1.6703
0.0000
0.0000

I g:gg~ I

~~gg

i 675

("I,

0 002
1 •
5.433 : 0.002
i 0.002
1 0 . 002
i 0.002

C
.,.,00
1500
1500

."'\

1500
1500
1500
1500

360

320
460

360

~65

i,0.002 I 1500!I 675
"" .002
0.002

318

A NONLINEAR DIGITAL OPTIMIZING PROGRAM FOR PROCESS CONTROL SYSTEMS

23
Nomenclature, Part 1

Note: The first part of this table defines symbols used in the descriptive
part of the text. The second part defines FORTRAN expressions
which have been used on the flow charts and also in coding the
program.

Summary of Problem B

B
CI

I - YI - Y2 /I 00 ~ 0

1- [(Y2- 1)/100]2-

B-1

0. 540

i'e

0."01 21192.5
".85 I 10.01
o.S9981 >.26'" 0.0002
0.02
t

go.oo

17477.5

0.60
30.00

0.540

199.15

0.06

I 211 .85 0.9Ooo! 1.2608
I 727.5
242.5 I 10.00
199.18

go.OO

0.10
0.8999 1.2605 0 .• 0002 5000
10.01
0.02
3.00
4250
0.06
2500
9.00 I 199.15

0.60
30.00

B_3 b

Eft'1c1ency
Cr1ter1on

Solut1on

00.60
30.00
90.00

B_2 a

(Y3/200)2~0

Starting
Valuell

-Yo

Test

Upper and lower bound functions, y': -Yu and Yu- Yu-

Constraint function.

Objective or value function.

HF, LF,
HN, LN

Designations of highest, lowest, feasible, nonfeasible
points in !!cunst:ralnt ' ! subprogram.

Proportionality constant.

Number of basic variables.

Y3/200~0

= -I + Y +

+
u

~()OOOO

Tallies

net

332

358
212
212

219

6110
330
413

323!

734
380
435

3971

511

74000
332500

0.0002 500000
0.0020 1170000
0.0059 330500

511

Tally on constraint function calculations.

Efficiency criterion, k

e
f

log2 Rmax'

Tally on value function calculations.

Gradient projection vector.

Number of constraint functions.
Parameter used in subprogram RIDGE.

Upper bound of each variable increased IOO-fold for this test

Ratio of range of y u to tolerance on y u'
b Upper bound of YI increased 100-fold; Y2 and Y3 increased 10-fold

max

Largest Ru'
Upper bound for y u'
Lower bound for y u'
Independent or basic variable"

Summary of Problem C
y
F =

52.909653- (YI- 0.5 Y2- 1. 0)2 -

2 (Y2- 2.04 YI

2. 072) 2_

3(Y3- 2 YI + 2.2)2_.4 (Y - 0.13 Y3- 1.618)2_ 5(Y - 1.5 Y3
I
2

O::!Oy.~2
1

C
C

(i = 1,2,3).
2
2
+ Y2
I

= (Y I

5.80- (Y

Test! Yo
C_O c 0.00
0.00
0.00

Fo
10.00

C_l d

10.00

C-2

I
1

C-3

1.6)2 + (Y 2

g:gg

10.00

0 • 00

10.00
0.00
0.00

10.00

)~O.

Subscripts

I. 5)2_

0.07~O.

0.10
0.10
0.10

Ye
1.800
1.600
1.400

Fe
52.910

0.10
0.10
0.10

1.673
1.246
1.200

0.10
0.10
0.10
0.10
0.10
0.10

Initial conditions.

Final conditions.

Efficiency
Criterion Tall1es

Solution

Start1ng
Values

0.00
0.00
0.00

Tolerance on first basic variable.

Basic step length for y u'
Set of all 6 •

+ 0.5)2 - 6 (Y - 0.196 Y - I. 0864)2
3

Operating vector (y I' Y2' ... 'Yk)'

,fe

Xorr.l'nclatur...:, Part 2

ne
296

0.001
0.001
0.001

2000
2000
2000

52.725

0.001
0.001
0.001

2000
2000
2000

296

1.675
1.246
1.200

52.724

0.001
0.001
0.001

2000
2000
2000

296

1.677
1.247
1.196

52.723

0.001
0.001
0.001

2000
2000
2000

290

nc1

BIG

325

C(K)
D(K)
DIN(K)
DORD(K)
EDGE

2 0
5
220

207

ENTER

264

FAIR
FENCE
FINISH

i'i
I

nf
230

con~trd.intl:i.

290
280
260

FOUL
No constraints in effect.

Constraint C I in effect.
Constraints C

and C in effect.
I
2
All constraints in effect.

Number beyond expected range of any variable (as 1030).
Constraint (bnction of Y).
Initial increments for Y(K).
Array for history of step sizes.
Signed probe length, K ranging from I to KY2.
Subroutine for 11follov.ri.ng tl a constraint or confluence of

JA
JAR(K)
JC
JCON(K)
JORD(K)

Subroutine for pablishing problem data and making initial
calculations.
Subroutine for pllblishing feasible advance.
Subroutine for calculating constraints.
Subroutine for publishing solution and making terminal
calculations.
Subroutine for publishing nonfeasible advance when seeking
a feasible point.
Index number of basic variable y(I).
JORD(I).
Variable affected in present probe.
Array of the eight subscripts for Y AR.
Number of specified constraint.
Order array for constraint calculations.
Order array for probes.

STUDY OF BUSINESS INFORMAnON SYSTEMS

Nomenclature, Part 2

KC
KERR
KEYC
KEY23
KORD
KVIOL
KY
KY2
MQD(K)
NC(K)
NCT(K)
NLIST
NP
NVAL
NVALT
OBJECT
ORDER
PROBE
RIDGE
SAVE
STEND
VAL
VALHFI,
etc.
VALS
Y(K)
YA
YAR(K)
YH(K)
YL(K)
YS

Number of constraints.
Error flag, numbered for statement which detects error,
or for selected types of errors.
I when seeking feasible point, otherwise 2.
2 to select Subprogram RIDGE, 3 to select Subprogram EDGE.
J, 200 or 300 in Subprogram PROBE, RIDGE, or EDGE on
SUCCEssful probe (other-.;..tisc 0).
I for nonfeasible, 2 for feasible point.
Number of basic variables.
KY + KY = range of JORD.
Array for discrete variables (MQD(K) = 0 if y(K) is a
continuous variable).
Tallies of constraint violations during major cycle.
Tallies of calculations for individual constraints.
Tally of listings (one per feasible advance).
Problem identification number.
Tally of VAL calculations during major cycle.
Tally of VAL calculations during complete problem.
Subroutine for calculating VAL.
Subprogram to set orders of probes and constraint calculations.
Principal probing subprogram.
Subprogram for "following" a "ridge".
Subroutine for calculating and storing quantities which will
be needed for VAL and/or C(K).
Final tolerance on step size for first variable.
Value function or objective function.
VAL at Y(JAR(I», etc.
Reference value of VAL
Basic variable.
Y(JA).
Array of the eight probes Y(JAR (1) ), etc.
for classification of critical probes.
Upper limit for Y(K).
Lower limit for Y(K).
Reference value of Y(JA).

See Figure 2

References

2.
3.
4.
5.
6.
7.
8.

9.
.Lv.

II.
12.
13.
14.
15.

16.
17.

N. R. Amundson, American Institute of Chemical Engineers, Tenth
Annual Institute Lecture, Cincinnati, December, 1958.
S. H. Brooks, "A Discussion of Random Methods for Seeking Maxima, "
Operations Research, vol. 6, p. 244; 1958.
R. Dorfman, P. A. Samuelson, R. M. Solow, "Linear Programming
and Economic Analysis," McGraw-Hill, New York; 1958.
R. O. Ferguson, L. F. Sargent, "Linear Programming Fundamentals
and Applications," McGraw-Hill, New York; 1958.
S. I. Gass, "Linear Programming Methods and Applications," McGrawHill, New York; 1958.
Clifford Hildreth, "A Quadratic Programming Procedure, " Naval
Research Logistics Quarterly, vol. 4, p. 79; 1957.
A. S. Manne, "Scheduling of Petroleum Refinery Operations,"
Harv:..rd University Press, Cambridge; 1956.
J. B. Rosen, "The Gradient Projection Method for Nonlinear
Programming; Part I, Linear Constraints, " J. Soc. Industrial and
Applied Math, vol. 8, p. 181, March, 1960; "Part II, Nonlinear
Constraints, " to be published.
T. L. Saaty, "Mathematical Methods of Operations Research,"
McGraw-Hill, New York; 1959 .
E. Si.t"l.gt:1, "Si.fllulatlu(l a.nd Optl:l;'-l~ .... a.tiO.r, uf Oil Refinery Dcsi g i"'l, II
Shell Development Co., Publication P-839, Emeryville; 1959
I. S. Sokolinkoff, and E. S. Sokolinkoff, "Higher Mathematics for
Engineers and Physicists" (Second Ed.), McGraw-Hill, New York; 1941.
Henry Stone, Per sonal communication.
Philip Wolfe, "Computational Techniques for Nonlinear Programs, "
Princeton Conference on Linear Programming, March 13-15, 1957.
W. S. Dorn, "Non-Linear Programming," Research Report RC-266,
IBM Corp., Yorktown Heights, N. Y., May 24, 1960.
R. E. Gomory, "Outline of an Algorithm for Integer Solutions to
Linear Programs," Bulletin of the American Mathematical Society,
vol. 64, p, 275; 1958,
R. Bellman, "Dynamic Programming," Princeton University Press; 1957.
R. E. Griffith, R. A. Stewart, "A Non-linear Programming Technique
for the Optimization of Continuous Processing Sy-stems," Management
Science, vol. 7, p. 379; 1961.

A NONLINEAR DIGITAL OPTIMIZING PROGRAM FOR PROCESS CONTROL SYSTEMS

STARt

READ AND
CHECK DATA

MAKE PRELIMINARY
IF NEEDED, FIND
CALCULATIONS.
~----DI A FEASIBLE POINT
LI ST RESULTS
AN 0 PROCE ED
AND PROCEED

STORE Hi-LO,
FEASI BLENONFEASIBLE 1 0 - - - - - - 1
POINTS AND
ALTERNATIVES

GO TO PROBE ,SEEK
IMPROVED FEASIBLE
POINT WITHOUT
REDUCING STEP
SIZE

\
\

I
I

\
SOME
NONFEASIBLE

GO TO RIDGE,
SEEK I MPROVED
FEASIBLE POI NT,
USING HIGH AND
ALTERNATE
FEASIBLE POINTS

\
\

RESET TO
BOUNDS WHEN
REQUIRED

GO TO EDGE, SEEK
I MPROVED FEASIBLE
POINT, USING HI -LO
FEASIBLE NONFEASIBLE
POINTS AND
ALTERNATIVES

LIST POINT
AND PROCEED

GO TO ORDER,
REORDER PROBES
AND CONSTRAINTS;
PROCEED

NOT BELOW
TOLERANCE

LIST
RESULTS

Fig. 1 Probe method for nonlinear
constrained optimization

t----........j;)(

I NTERUPT,
STOP, OR
RELOAD

STUDY OF BUSINESS INFORMATION SYSTEMS

START

INITIALIZE
VALH'S AT-co
VALL'S AT+co
KEY 23 2,
I =I

SUBSCRIPTS FOR
CRITI CAL PROBES

I
2
3
4

SELECT AND
SAVE VARIABLE
OF PRESENT
PROBE Y(J).
INCREASE OR
DECREASE AS
REQUIRED.

5
6
7
8

* SPECIAL
PROCEDURE FOR
DISCRETE VARIABLE IS

ACTIVATED BY MQD

TEST BOUND
RESET TO
BOUND IF NEEDED

,----------It>!

UPGRADE
HF2 , t!£.J;
IF VALLF I
OR VALLF2=co
UPGRADE
LFI OR LF2

COMPUTE
CONSTRAI NTS
AND TEST.

SET
KEY 23

HFI
HF2
LFI
LF2
HN I
HN2
LN I
LN2

UPGRADE
HF2, HFI ;
IF VALLN I
OR VALLN 2 =00,
UPGRADE
b!:!.1 OR ~

Fig. 2 Subprogram PROBE

RESTORE

I
I

A NONLINEAR DIGITAL OPTIMIZING PROGRAM FOR PROCESS

CO~TROL

, F=4
I
I
Q,

SYSTEMS

,
\

\
I

CONSTRAINT
C2 (YIIY2)=O

BOUND
Vt- Y1=O

----+-----------------------~~--+----BOUND

Y2- V2-=O

Fig. 3 Operation of subprograms
PROBE and EDGE

STUDY OF BUSINESS INFORMATION SYSTEMS

START

COMPUTE
MIDPOINT

COMPUTE ALL
CONSTRAINTS

I
COMPUTE

VAL=
LEAST C(K)

IQ------\

INITIALIZE
KSW 2=0

1-----01

COMPUTE
CONSTRAINTS.
TEST

CALL
OBJECT.
CALCULATE

VAL.

SET
KSW2
~

SET
KORD

= 200

1---------+----01

l
Fig. 4 Subprogram RIDGE

APPROXIMATE TO
PARABOLIC MAXIMUM.
Y(JAI)= (I.O-RISE)
Y(JAI) + RISE
YAR (I).
ETC_
.

A NONLINEAR DIGITAL OPTIMIZING PROGRAM FOR PROCESS CONTROL SYSTEMS

Y(2)

F=3
F=4

--+-------------------~

Fig. 5

Operation of subprograms
PROBE and RIDGE

LN
(D)

C=O
/CCC "HC Ju.i:>".1.1.1I.,;a.".1Vll

v.!

.1".

TT ............ 11 __
:..c
Ui:>u.a..1.1Y,.1.1

. . . . _ . . . . ___

vue

-l~

... _.L .....

I.,;Vl1UUI.,;\,;:;

an experiment, one has some definite idea in mind
which he wants to test. Once the experimental
apparatus exists, the main task of the experimenter
is taking data. In our case, the most important
function of the experiments is to get a feeling for such
a system, for how it works, and what its possibilities
and limitations are. Once the experimental apparatus
exists, the main task of the experimenter is to play
with it. From the experiences gained thereby, he will
be able to form specific ideas which he then tries out
by building a new system. By playing around with the
new system, he will get new information about what is

wrong with it and again try to improve it. This procedure not only tests any ideas, but its results provide a
guide line for the next step, and both of these contributions, the testing of ideas and the catalytic action of
generating new ones, are acutely needed in this work.
With these ideas in mind, we proceeded to build
the necessary apparatus. The MH-l system consists
of the TX-O computer, a control unit and a servomanipulator. The TX-O was chosen because of the
flexible in-out equipment and because of its availability
(the total computer sign-up time was in excess of 500
hours). Since for several reasons interpretive programming techniques were used throughout the work
(the speed of operation is determined by the external
equipment and not by the speed of the computer), the
relatively small memory capacity (8000 words, 18 bits
each) of the TX-O never even came close to exhaustion.
The control unit selects the motors and sense
organs according to the computer instructions, and
generates the servomotor voltages. A block diagram
of it is shown in Fig. 1. The unit contains 150
transistors, 300 diodes.., and 28 thyratrons, and
occupies almost two-thirds of a relay rack.
The mechanical arm consists of a motorized
American Machine and Foundry Servomanipulator,
shown in Fig. 2. Each of the seven servomotors
drives one degree of freedom, and one potentiometer
is coupled somewhere to each degree of freedom. Lowquality low-resolution potentiometers are used because
it is felt that organisms do not have a very accurate
sense of position. Whenever possible, we tried to
imitate the properties of living systems when similar
design decisions had to be made, since after all the
animal system is an existence proof of the solvability
of our problem.
More important than the sense organs for position,
are the sense organs for touch which are spread all
over the hand. The hand is shown in Fig. 3 and explained by Fig. 4, as far as the nature of the sense
elements goes. A binary sense of touch is satisfactory,
since the applied forces are better determined in a
quantitative way by determining the motor input instead of the pressures exerted on the sense elements.
Notice that all the possible fredback loops go through
the computer.
The job of building the equipment took the better
part of the year 1960. The mechanical part and the
motor action of the hand did not present any novel
problems, and neither did the control unit. But considerable experimentation and modification was needed
in the construction of the sense organs, as our philosophy of their operation and function changed gradually
during the ex-perimental phase, and major changes
would have had to be made in the sensory apparatus if
the work had been continued beyond that reported here.

THEORETICAL PROBLEMS IN ARTIFICIAL INTELLIGENCE
DESCRIPTION OF SOME EXPERIMENTS
MH-l has gone through several states of increasing program sophistication. We shall describe some
of tlle eA--periments with the last programming system,
and follow it up with the explanation of the underlying
principles.
In order to be able to evaluate the progress made
with the different programming systems, we chose one
standard activity for MH-l: To play with wooden
blocks and boxes. MH-l builds small structures out
of these blocks, or puts them away into the boxes.
The following program, for instance, will locate a
box on the working table a.fld then grope for the blocks
and put them into the box.
Program No.
Instructions
1.

goto ml,mL
scan ml,md

3. goto m2,mL
4. scan m2,md
5.
6.
7.
8.

take m2,hld
goto ml,mL
put ml, mL+ xb+ yh+ zd
goto m2,0

Description
locate box (mL)
determine size and location of ml
grope for blocks (m2)
determine size and
position of m2
take the block and hold it
go to ml with m2
put m2 into ml
go to the former position
of m2 and grope for new
block

9. transfer to 4
In more detail, the following events occur during
the 9 phases:
1. MH-l starts a searching motion for an object (the
box) which it will call ml after it has found it. If ml
should have been scanned earlier, it would go there
directly.
2. MH-l determines the absolute position of ml so it
can find it again later, it determines its position with
respect to the hand and its size with respect to the
maximal finger opening, so it could grasp it if this
were demanded.
3. MH-l goes back into a search routine, groping for
m2 (the blocks). If it should run into m2 on its way
back to the initial search position, it would skip the
search phase and proceed directly with 4) . Generally,
if an obvious short-cut exists, MH-l will take it. On
the other hand, if something has not been done properly, MH-l will repeat it. For instance, during the
search procedure MH-l makes sure periodically that
it does not search too far above the table, since the
blocks are only t\.vo inches h1gh, Should it ever bump
into the table during the search action, it will interrupt the progress, repeat the check for proper heights,

MH-l, A COMPUTER-OPERATED MECHANICAL HAND

and then proceed.
4. MH-1 determines the position and the size of m2.
Scan routines can be avoided if the corresponding
information is given to the computer by the programmer
in a " setmodel" instruction.
5. MH-1 grasps the block and holds it. The method
used will depend on size and location of the block,
facts which have been determined in 4.
6. During that period, MH-l will move into the
vicinity of the box ml, and feel around for it until it
bumps into it.
7.

It will deposit the block into the box.

8. It will start to look for a new block, beginning
about where it found the previous block which is now
in the box.
What will happen if more severe trouble arises
than the kind which can be eliminated by simple shortcuts and repetitions? Notice that Program No. 1 contains no explicit information whatsoever about what to
do if difficulties arise. Should MH -1, for instance,
run into the box while looking for blocks, it will grasp
it and will get fouled up trying to put the box into itself. It does not realize that the box it takes is the
same object as the box it is supposed to deposit its
findings in. The reason is that rn2 can be any object,
not only blocks. If we want to limit m2 to blocks, we
have to say that at the beginning, and the corresponding
program will then look like this:

location after it has found it, somewhere on the side of
the table so as not to be in the way during the search
for the blocks. If one now takes the box away and puts
it back into the path of the block-search, the hand will
put the box back where it belongs and then continue.
It is evident that in some cases the hand really does
the reasonable thing if unexpected disturbances of a
considerable logical complexity arise, without having
to be told so explicitly by the programmer. How
successful it is depends, as we have seen, somewhat
on the form of the program.
Once in a while, MH-1 will, however, do something that does not make any sense at all, and, if it
does not check that itself, it may have to be interrupted manually. This happens about once in five
successful operations, such as putting a block into a
box. The reason for this is that the computer has
made a wrong decision when it was confronted with
an unexpected situation. Typically, it might then
shove away the box, kick over a block, or search at
a wrong place. However, the general performance is
quite satisfactory, and there is usually quite some
suspence built up among the spectators which releases
itself in applause when the first block is dropped into
the box.
Another program builds a tower out of the blocks
by piling them on top of each other. This is quite
interesting to watch because the growing tower sooner
or later collapses. All of these programs are quite
simple to write, as Program No.1 shows. A small
input routine permits it to write them directly into the
machine with the on-line flexowriter.

Program No.2
PRINCIPLES OF THE PROGRAMMING SYSTEM
setmodel m2, hor
goto ml,mL
scan ml,md
goto m2,mL
take m2,hld

this tells that m2 is a
small obj ect

no scanning of m2 required now, since its
size has been established
by the setmodel instruction

gutu ml,mL
put ml, mL+ xb+ yh+ zd
goto m2,mL
transfer to (take m2, hId)

With only this program modification, MH -1 would
not grasp the box if it runs into it a second time, even
if the box had been removed from its original place
and deliberately put into the path of the block-search
program. MH-1 would instead remember the new
position of the box and start the search for blocks all
over again. In still another, slightly different program, the hand deposits the box at some standard

We have seen that MH-l has made considerable
headway towards coping with difficulties by itself
without burdening the programmer. How is this
achieved?
Several levels of interpretive programs are used.
The computer contains a description of the objects in
the real world (model), indicating their absolute and
relative position and their size. These descriptions
..... _ _ _

i::I.n~

________ J

•

..,

gener,U"tlu

1___

.L1 _____________________

_ _, _ " ,

uy Llle !Jrugri::l.ll11Uer uy "::seLHluuel"

instructions, or automatically by the "scan" program
and always when the hand gropes for an object. The
interpreter for the highest program level (such as
described in Program No.1) has to find a routine in
memory which corresponds to:

1. the type of action (go to, find, etc.) demanded
2. the type of object concerned, as determined by the
model of this object

3. the goal specified in the program (hld=hold,
mL+ xb+ yh+ zd=on top of)
A typical routine would be one which grasps small
objects to the right of the hand. Each routine is described in a list that the interpretive program scans in
its search for appropriate routines. These routines,
in turn, are sequences of statements indicating desired
states of sense organs. One statement may concern
many sense elements. A typical statement might be
that the outside of the left finger should touch something. The interpreter of these routines determines
symbolically which motors will have to be energized
and how much in order to bring about the desired state
of these sense elements. This motor assigIll--nent may
depend on the position of the hand. The symbolic
motor commands thus generated are then interpreted
on the lowest level by routines involved in the position
and speed-control loops, by stop routines, timing
routines, and several error-checking and interlocking
routines.
The interpreter of the desired sensory state level
in addition to generating control commands for the
motors, creates a list of sense organs that are expected to change during that phase. Periodically, all
remaining sense organs are checked for changes and if
such an unexpected change should occur, the normal
program execution is interrupted. A special routine
then begins to determine what should be done about that
unexpected occurrence. There are three alternatives
that this routine can take.
First, it finds out whether these unexpected
changes are intended changes in the near future (by
looking ahead in the program) or if they did occur in
the near past (by looking back in the program). If
either one of these conditions is fulfilled, control will
be transferred to that program location and the program
will continue from there on. This is the basis for the
mentioned behavior of MH-1 with respect to obvious
shortcuts and repetitions of unsatisfactorily performed
actions. But one can easily see that there is a chance
that the interrupting unexpected change occurs as an
intended change in a completely different connection,
and then it is unlikely that the corrective action taken,
namely, transferring control to that program location,
will be successful. The occurrence of this can be
minimized by not letting the interrupt program search
in too distant parts of the routines, and certainly not
in different routines. Sometimes, however, the
corrective action taken will be wrong, and in most
cases there will then be another interruption. But
that is usually too late because by that time MH-1 has
lost track of the original goal, since there is no return to the original program once the interrupt program has found a spot that seems to be appropriate to
the type of interruption. This is what has happened
when MH-1 starts to do something that appears illogical from the outside.

THEORETICAL PROBLEMS IN ARTIFICIAL INTELLIGENCE

The second alternative is adopted if no such
intentional occurrence of an unexpected sense change
can be found. If the program is in a "take'! phase,
this phase will be interrupted, and the scan program
will be started. \,Vhen the nature of the disturbing
object is discovered, another special program will
look up the highest level program and find out whether
a similar object is ever mentioned there. If so, control will be transferred to that location of the program.
This is the explanation of the phenomenon that in the
block and box program the box can often be encountered
a second time without any disastrous consequences if
MH -1 realizes that it is running into the box again and
that it is not supposed to. It will simply switch back
to that part of the program in wp..ich it dealt with that
box.
Third, if no appropriate instruction can be found
in the highest program level, and whenever an interrupt search is unsuccessful in a phase other than
"take", the hand will withdraw until the disturbance
disappears, and then continue what it tried to do
before, repeating this several times if necessary.
It would be nice if it were possible to have a
program generate a corrective program itself in the
case of interruptions, but the present sense organs
make this impossible except for simple motions like
withdrawing. The present sense organs are satisfactory if used together with a program \r"Titten by
somebody who knows what the hand is supposed to do,
but they are not sufficient to determine a reasonable
sequence of subgoals, expressed in terms of sense
elements, with respect to some over-all goal. To
give an example of this, it is possible to program
MH-1 in such a way that it will detect the edge of an
object, by performing a few test motions with the
fingers. But the sense output makes sense only in
connection with the knowledge of the idea behind those
test motions. If the hand were to. move by itself and
you had only access to the sense output, and nOL to
the intention of the programmer, you would not be able
to detect the fact that the hand has just run over the
edge of an object. This is why the automatic generation of routines is not possible with the present sense
organs.

So much for the design of the programs which
achieve the present degree of independence of disturbances and which permit the present, conveniently
vague way of specifying a program. In the following
discussion we shall take a second look at all this, but
from a somewhat more fundamental point of view,
using less of the terminology of computer programming.

AWARENESS AND UNDERSTANDING

We have to distinguish between the computer and
the real world. The computer-internal world consists

~H-l,

A COMPUTER-OPERATED MECHANICAL HAND

of the models (descriptions) of some of the real-world
objects, the higher level programs, and the registers
containing the present sense input. The models are an
abstract image of the real world, the programs represent the intentions of action of the hand in the real
world, and the registers containing the sense input are
that part of the sensory apparatus to which the computer has access. It is important to understand how these
things are interrelated.
The internal world is the only tp.ing upon \vp.ich the
computer can operate directly. Mere existence of
objects, relations, and conditions in the real world is
not sufficient. Unless these can be projected into the
computer-internal world, they are neglected by the
computer. Therefore, if we want to couple a system
with mechanical intelligence to the real world, we have
to make sure that the computer contains an internal
representation of the external world which is sufficiently complete. The task of the sense organs is to
transfer information between these two worlds. To
give an example of this, the internal world of MH-l
contains a complete representation of everything
touching the fingers, and it can, therefore, be programmedto interrupt its activity and decide on a
better course of action if something touches the fingers
unexpectedly. However, MH-l has nothing in its internal world which indicates progress. MH-l will,
therefore, not complain if a poorly written program
takes half a dozen attempts to achie.ve its purpose,
grabbing a block for instance.
A good internal world and good sense organs will
permit the mechanical imitation of what in psychology
is called "awareness". The design of a sufficiently
complete internal world is probably the most difficult
problem in this computer-real world symbiosis. A
computer cannot be aware of phenomena that are not
reflected in its internal world, and cannot bring its
"intelligence" to bear upon them.
Awareness, however, is not all that is required
for the coupling of an intelligent machine with the real
world. The machine must be able to correlate the
processes in the real world with the operations performed in the internal world and vice versa. We shall
call this ability !!understanding the two worlds". Let
U::> nOw 8ee what form this understanding takes in MH-l.
Let us assume that the sense organs have detected an
unexpected change, and that the machine is now aware
of it. Understanding is required if the machine is to
find a way out of this situation by means of processes
in its internal world because it must be able to relate
the processes performed in the internal world and
those in the outside world. MH-l, for instance,
assumes that hand actions are responsible for any
unexpected change. It, therefore, looks up the
representation of its actions in the internal world,
namely, its program. It determines which part of
that program might bring about such a change in the

45
environment as the one which caused the interruption.
Without performing the action, MH-l is able to understand what its program means with respect to the outside world, and, therefore, to the sense input. To
find an appropriate passage in its programs, and to
transfer control to that part of the program, will often
solve the difficulty.
Comparing the action plan (program) with the real
world is only one form of understanding, comparing
the models \vith the real VvTorld is another, and this
form is used in the second of the described types of
interrupt action. However, it follows from the structure of both of these processes of understanding that
MH-l would be at a loss if it was confronted with a
living world, where things change of their own accord,
not only because of actions of MH -1. A different form
of understanding would be required to cope with the
problems of such a world, a form that takes into
account the dynamics of the real world.
MH -1 is not very advanced in the development of
its power of understanding, but I do think that it is at
least a step in the right direction.

THE SENSORY APPARATUS
We have not said much about the sense organs,
although it became evident during the experimental
phase that we had much to learn about them. We
became aware of their importance concerning the
programming language. In an earlier system, the
routines were written in terms of the motors to be
used at each element of time. Since the coordination
of the sense of touch with the motor organs depends
on the position of the hand, it is quite easy to see that
it would be rather difficult to scan such a program for
an interrupt condition.
In classical control systems, the sense elements
translate the stimuli originating in the real world into
the system-internal signal form, an electrical current,
a mechanical displacement, and so forth. In MH-l,
the programming language corresponds to the signal
form in a classical system. On the mechanical hand,
the task of the sense organs is therefore to match the
external stimuli to the programming language. This
difference in tasks results in sense organs that are
different from those usually found in control systems.
There, sense organs, or transducers, generate one
specific signal with one specific purpose, for instance,
they detect the temperature at one place. For the
hand, we need distributed sense organs, something
like our skin. The output of each microelement is
only a small part of the pattern composed of the output of all of the microelements. This pattern forms
a word in one of the interpretive languages, and it is
this whole word which is of importance, which conveys information about the real world and upon which

THEORETICAL PROBLEMS IN ARTIFICIAL INTELLIGENCE

as a whole the computer works. Each single sense
element has a much less specific task of its own; what
it really does is determined by the process the computer applies to the received words, and not by the sense
element.
The construction of this type of sense organs, or
rather ensemble of sense elements, is a novel problem
of which we became aware late in the project, and for
which we do not have any solutions yet. The sense
elements in Fig. 4 are only an unsatisfactory substitute.
This new approach to the construction of the sensory
apparatus would have been the next step if the project
had been continued beyond the work reported here.

APPLICA TIONS
This work is of interest with respect to two
possible applications: The construction of mechanical
hands as useful tools, and the exploitation of the philosophy behind the control problem.
Mechanical Hands for Industrial Applications
There has been a considerable interest in generalpurpose programmable tools of the form of a human
arm and hand. 2, 8 The difficulty seems mainly one of
cost, since the demand falls off rapidly if the price
rises above $15,000. This is an order of magnitude
less than the cost of a computer alone which would be
required for a system similar to MH-l, This difficulty
could be partly relieved by having one computer control several mechanical hands at a time, and by having
functions, which are now performed in a routine fashion by the TX-O, delegated to less expensive analog
equipment that would go with each hand. The computer
would then enter the picture only when something has to
be decided which is beyond the power of the equipment
that goes with each hand; instead of really controlling
all of the hands all of the time, the computer would
only supervise them.
In general, it seems that the more universal a
tool becomes - and a mechanical hand is meant to be
universal - the less qualified is the work the tool is
supposed to do, at least in production applications.
This is probably the reason behind the mentioned price
squeeze, and besides it raises serious doubts about the
desirability of such machines in the present labor
market, which consists of a surplus of unqualified
labor and a shortage of qualified forces.
Mechanical Hands in Hostile Environments
We are talking about the very problem that gave
rise to the appearance of servomanipulators: Manipulation in radioactive areas. Other adverse environments may be found in deep-sea exploration and space
exploration. This situation is radically different from

the described production situation because under these
circumstances even very simple actions become
highly qualified ones. However, there is still no
economical or technical advantage to be gained from
replacing the hwuan operator of such a manipulator by
a computer, except in one case. The manipulator may
be so far removed from the human operator that
communication with it becomes difficult, either because of delay or because of the power required to
ensure a reasonably good transmission. This situation arises in space exploration. One way to solve
this difficulty is to send some mechanical intelligence with the manipulator, in the form of a computer.
One can easily see that the transmission of a program
like the one in our example is much easier than the
establishment of a complete, real-time telecontrol
system, besides solving the nasty delay problem. Including the apparative delays (scanning rate of the TV
system) it is estimated that the delay in a control loop
extending to the moon would be approximately 3 seconds. Assume that the manipulator should pick up a
rock on the moon. The operator will see that the hand
is in the appropriate position only 1-1/2 seconds after
this event occurred. Another 1-1/2 seconds will pass
until the signal to stop reaches the manipulator. Unless the manipulator works very slowly, it will have
moved beyond the rock by that time. But, if there
were sufficient intelligence incorporated into the
system on the moon, we would simply line up the
ma..'lipulator and then tell it to go forward until it
touches the rock, similar to the actions that are
taken by MH-l when it searches for objects.
The cost of providing that mechanical intelligence
is irrelevant in similar applications. It might even be
that the accompanying simplification of some of the
other communication equipment more than makes up
for the cost of the computer.

APP LICATION OF THE
PROGRAMMING PRINCIPLES

I am mainly thinking now of the accessibility of
some non-human environment to the computer in order
to enable it to use the described forms of awareness
and understanding. We have only begun to scratch the
surface of this problem, and it will probably remain
in the research stage for some time to come. This
research will have to proceed in two directions:
1. Development and construction of the required
sense organs. It would help greatly if we could build
an eye for something like the MH-1 system.
2. Development of the necessary internal worlds, for
instance, better models and better ways to generate
them. This research will be interesting both from a
human and from a technical point of view.

MH-I, A COMPUTER-OPERATED MECHANICAL HAND
Although the exploitation of this research may be
farther off than the construction of programmable
mechanical hands, I think that ultimately it is far more
interesting. It seems difficult to build a mechanical
hand that will surpass our own human hand. We can
easily surpass some of its properties, but that is
easier accomplished with special-purpose equipment
than with something as general as a hand. However,
am optimistic enough to think that a better fundamental
understanding of our human information processing
will open all kinds of doors for interesting technical
applications. I, therefore, consider any contribution
made by the study of MH -1 in this area to be more
important.

REFERENCES
1. Alfred Chapuis, Edmond Droz, "Les Automates.
Figures ArtificieUes d'Hommes et d'Animaux",
Editions du Griffon, Neuch~tel, Switzerland; 1958
2. H. W. Nidenberg, "Programmed Manipulation:
Noman", Technical Report, Advanced Manufacturing
Engineering Service, March 15, 1960
3. John W. Clark, "The Mobot, a Fully Remote,
Mobile Handling Device", Technical Memorandum 627,
Hughes Aircraft Company, November 27, 1959
4. "Automatic Programming of Numerically Controlled Machine Tools", Final Report 6873-FR-3,
Electronic Systems Laboratory, MIT.
5. R. Tomovic, "The Human Hand as a Feedback
System", International Federation of Automatic Control, Moscow, 1960, vol. 2, pp. 1119. (Translation
by Butterworth's Scientific Publications, London)
6. "Electro-Mechanical Manipulator for Remote
Handling", Automation Engineering Department, Borg
Warner Corporation, 1956

t - - - -....

directional control

c.om~an<}---JmOtOr-1

motor
hold CirCUit

•
fI

,0---.
1
1-

6
L-________ .__________

TX-O

H·:

I
I

Jjve register

I
I

:
1
1

~____~:____

7 units

_r-,

motor comman~
hold circuit _j~

(in-out
register)
L8 bits

sense organs

51J

sense organ selector

....,
::z::
trl

::0
trl
....,

(=)

transfer
on level

t""

A-to-D converter

operate
pulses

'"0

::0

ot:J:j
t""

trl
~

Z
>-

Fig. 1.

Block diagram of the MH-l control unit.

::0
....,

(=)

>
t""
Z
....,
trl

t""
t""

21trl
Z

trl

MH-I, A

CO~fPUTER-OPERATED

Fig. 2.

MECHANICAL HAND

The servomanipulator. The part toward the reader is the active
arm, the second arm serves only for balancing purposes and
carries the servomotors.

THEORETICAL PROBLEMS IN ARTIFICIAL INTELLIGENCE

Fig. 3.

The mechanical hand.

MH-1, A COMPUTER-OPERATED MECHANICAL HAND

Fig. 4.

The sense elements on the hand.

(1)

switch closing if touched; detects position of objects between
fingers; binary output.

(2)

a total of six contacts (2 per plate) closing if touched;
indicate contact with finger surface; binary output.

(3)

6 pressure elements in rubber pad; detect firmness and
location of grip; continuous output (variable resistance).

(4)

photodiode; reacts on shadows cast by black objects;
continuous output.

(5)

2 pressure pads as in (3).

(6)

pressure element on bottom of wrist; closes when hand
rests on table; binary output.

Elements (2), (3), (4), and (5) appear on each finger.

5.3

AN ABSTRACT MACHINE BASED ON CLASSICAL ASSOCIATION PSYCHOLOGY

Richard F. Reiss
Lihrascope Division
General Precision, Inc.
Glendale, California
Summary
The theories of classical association psychology (circa 1750-1900) attempted to explain
human thought processes in terms of certain mechanistic forces operating on discrete entities
called "sensations," "images," and "ideas." Although these theories have become unfashionable
since the turn of the century, due primarily to
their ambiguity and the difficulty of experimental verification, and whereas they may never
prove adequate for human psychology, it is possible that they may, nevertheless, provide a
fruitful basis for some types of artificial intelligence. One method of exploring ramifications of the classical theories is the formulation of an abstract "machine" which constitutes
an interpretation of the theories and whose behavior can be examined in any desired detail. In
this paper such a machine is partially constructed, and some of its behavioral features and problems are discussed.
Introduction
The general problem of synthesizing intelligent artifacts is sufficiently broad and difficult to justify a variety of research strategies. One such strategy is to select a psychological theory, however inadequate (as they all
are), and examine it for useful ideas and insights. This strategy has been used in the
studies on which this paper is based.

any theory that could not quantify its concepts
and be subjected to precise experimental testing.
Associationists were unable to meet these criteria successfully, and the classical theories in
their general forms were rapidly abandoned. we
say theories, rather than theory, because associationists rarely agreed on more than a few basic
concepts. Later we shall simply refer to "the
classical theory," by which we mean those concepts that did receive widespread acceptance.
Some of these concepts are to be found, frequently disguised by new terminology, in many contemporary schools of psychology. But the old theories with their sweeping assumptions have been
effectively dead for 50 years.
The problem of artificial intelligence provides a distinctively new framework for evaluating psychological theories. If one is concerned
with the subproblem of mechanizing human thought
processes as they actually occur, then of course
the validity of a psychological theory is of
great importance. The general problem, however,
does not require such stringent criteria; the
search is for suggestive material, in whatever
form.
The association theories are of interest on
three counts: they were produced by several brilliant minds struggling through introspection with
the problem of mind; they involve the action of a
few mechanistic forces operating on discrete entities; and they aim at explaining the higher
thought processes. Unfortunately, the associationists made no sustained attempts to quantify
their assumptions and search out the detailed
consequences. This must be done, then, for the
first time (to my knowledge), and the resulting
abstract machine represents just one possible interpretation of classical theory. Another interpreter might well produce a machine that differs
in many respects. Some alternatives will be
noted in the discussion below, but in general the
postulates will be introduced without apologies
or historical justifications.

Classical association psychology was developed primarily in England and enjoyed considerable popularity for more than a century (circa
1750-1900). Space does not permit even a brief
recount of its history, but some of the key works
will be mentioned for purposes of reference. Although Aristotle vaguely recognized the minimal
association principles (see Hami1ton 8 ), the modern development of association theory began with
some hypotheses laid down by the British philosophers Hobbes 10 , Locke 13 , Berke1ey5, and Hume 11 .
They were, however, concerned primarily with ~
epistemology rather than psychology. Hart1ey~ is
generally considered to be the founder of associationism as a psychological doctrine, and it
flowered during the 19th century due largely to
the efforts of Brown 7 , James and John Stuart
Mill 14 ,15 and above all Bain 1 ,2,3,4 and
" a detailed history, see Warren 19 •
Spencer 16
For

From Hartley on, associationism was generally tied to parallel theories of the nervous system. In constructing the abstract machine, this
facet of association theory will be almost entirely ignored. Except in the concluding remarks,
the problem of physically realizing the abstract
machine will likewise be ignored.

Association theory proposed to explain the
highest levels of conscious thought processes,
perhaps the most elusive of all experimental subjects. By 1900, the revolutionary development of
physiological and experimental psychology had
created an atmosphere which was very hostile to

The objectives here are simply to show what
a machine based on association theory might look
like, to demonstrate some of its behavioral characteristics, and to raise problems that appear
important to further research along these lines.
Our strategy in this project has been to strive

THEORETICAL PROBLEMS IN ARTIFICIAL INTELLIGENCE

for a reasonably complete machine without regard
for our ability to analyze its behavior; we hope
thereby to avoid the premature selection of problems that appear interesting but are actually
trivial: The nine postulates (together with subordinate assumptions) which are discussed here
fall far short of a complete machine. But combined with remarks on further postulates in the
concluding section, they should be adequate for
the purposes of this paper.
The postulates will be introduced in three
groups. After each group has been st ated, some behavioral consequences of that group will be examined in detail and a few generalizations ventured.
The Four-Postulate Machine
The first four postulates form a group which
produces a basic machine without sensory inputs
or motor outputs. Tne behavioral potentialities
of this machine must be examined in some detail
before proceeding to further postulates.
Postulate PI:

There exists a finite set M of
"memory tokens" ml , m2 , •••• , mp •

Initially we make no assumptions whatever regarding the nature, structure, or properties of
these tokens although they obviously represent
hypothetical entities--such as "images," "ideas,"
"impressions," "concepts" with which the associationists furnished the mind. The number of memory tokens, p, is assumed constant; and we do not
inquire into the origin of these tokens at present.
Postulate P2:

Between each pair of memory tokens,
mi and mj' in M there are two
"bonds" whose "strengths" are
given by "coupling coefficients."
The bond from mi ~ mj is represented by the coupling coefficient
Cij; and the bond from mj ~ mi,
by Cji.

mj" will mean that CiYO. All coupl~ng
coeff1c1ents are assumed to range over the POS1tive real numbers, with a lower limit of zero and
no upper limit specified at present.

bonde~

Postulate P3:

There is an "attention register"
which can hold a set A of memory
tokens. The maximum number of
tokens in A is A, and this integer
will be called the "length" of the
attention register.

The introduction of the attention register
completes the hardware of the four-postulate machine. It will be assumed that A« p and that A
is, therefore, a proper subset of M. The intent
of the adjective "attention," if not immediately
apparent, will become clear in the course of discussion. In this paper, A will be considered an
independent vari able, or parameter, of the machine.
Before stating the fourth postulate, it will
be necessary to introduce a special function and
a related set. For every memory token mi we define the adduction function fie If mi is a member of A, i.e., is in the attention register,
then fi=O. If m is not a member of A, then the
i
value of fi is g1ven as
fi

=~Cji

(1)

where j ranges over the subscripts of tokens in A.
Thus if mi is not in A, fi is the sum of the coupling coefficients of ponds from all tokens in A
~ token mi'
In terms of the coupling matrix, fi
is the sum of all those elements in the j th column, which are also in rows corresponding to the
tokens in A.
The adduction set F is defined as follows:
memory token mi is a-;ember of F if, and only if,
there exists no memory token m· for which f· > f· .
In other words, the adduction ~et is compos~d ot
the token(s) having the largest adduction function
value(s). Be it noted that F cannot be empty; indeed, if all coupling coefficients are zero, F:M.

TIle "bonds" il1troduCed by P2 are first ap-

proximations to the associationists' "connections"
and "attractions." Although the associationists
seem to have generally assumed that connections
are symmetrical in the human mind, it was and is
a point of controversy; and we here take the more
general case where the bonds from mi to mj and
from m) to mi are treated as independent entities.
It wilL be seen later that these bonds must, in
turn, be split into two components.
The coupling coefficients may be organized
to form a square (p x p) matrix where ci· is the
element in the i th row and j th column. this will
be called the coupling matrix and will be denoted
by "(cij)'" Digraphs will be used to illustrate
small token groups. Figure la shows a system of
five memory tokens, and Figure lb is the equivalent coupling matrix. It will be noted, in the
graph, that bonds with zero coefficients have
been left out and that symmetrical bonds (as between m2 and m4) are represented by a single twoheaded arrow. The statement that "mi is not

Postulate P4:

Every at seconds a memory token is
chosen at random from the adduction set F and entered into the
attention register, i.e., set A.
If the attention register is already filled, then the "oldest resident" will be simultaneously
ejected.

This postulate introduces action into the
abstract machine. The state of the machine at
any moment is defined by the coupling matrix and
a list of memory tokens in the attention register.
Every at seconds the machine changes state by entering a memory token into the attention register
and ejecting the token that has been longest resident in the register. It will be assumed that
all members of the adduction set F, at any moment,
have equal chances of being selected for entry
into set A; i.e., if there are n members of F, the
probability that any particular member will be
selected is lin. If F contains only one member,

AN ABSTRACT MACHINE BASED ON CLASSICAL ASSOCIATION PSYCHOLOGY

then the next token to enter A is uniquely determined.
Yne sequencing of tokens through the attention register mayor may not be a stochastic process, depending upon the nature of the coupling
matrix. For example, if there is exactly one nonzero element in each row and column, then the machine's behavior for all future times is precisely
determined by the tokens initially placed in the
attention register. On the other hand, it is easy
to formulate any number of coupling matrices which
produce stochastic behavior. It should be noted
that the coupling matrix is not a Markov matrix;
the coupling coefficients are not transition
probabiH ties.
Discussion of the Four-Postulate Machine
The first four postulates produce a class of
machines which clarifies certain problems and potentialities inherent in classical association
theory. The sequencing of memory tokens .through
the attention register might be interpreted as a
first, crude approximation to the flux of ideas,
images, etc. into and out of the conscious state.
The associationists generally believed that thought
processes are conscious processes and that introspection is, therefore, a powerful tool for the
analysis of thought. As Bain 4 put it, " ••• Introspection is still our main resort--the alpha and
omega of psychological inquiry: it is alone supreme, everything else subsidiary. Its compass
is ten times all the other methods put together,
~~d fifty times the utmost range of Psycho-physics
alone." By the time Bain died (1903), evidence
was rapidly accumulating in favor of the thesis
that subconscious processes influence thinking to
a remarkable extent. This development, compounded
by failing attempts to make introspection a precise analytical tool and various other trends (see
Boring's hist ory 6) led to a widespread rejection
of introspection. It seems the associationists'
theory had become so closely connected to the introspective technique that, when the technique
was discredited, the theory was discredited too.
Actually the failures of introspective technique
show only that the association theory is difficult
to test, not that it is invalid. It is by no
means necessary to assume that all, or even most,
association processes occur at a conscious level.
In fact association theory has survived (in a simpler form) in theories of conditioning and learning which ignore consciousness altogether.
Since we are not concerned here with the
validation of a psychological theory, and since
consciousness is not in any event a necessary constituent of association processes (although the
classical associationists failed to recognize this
fact), we shall not postulate any relations between consciousness and the states of our abstr~t
machine. As a consequence of P4, a memory token
must be in the attention register in order to influence the behavior of the machine. Nothing
more is to be read into that postulate unless it
amuses the reader to do so.

Postulates P2, P3, and P4, taken together, are
the result of a difficult decision that must be
made in any interpretation of the classical theory.
At times the associationists spoke of the connections between mental entities as though they were
little more than indicators of possible, or preferred, sequences among which some higher agency
chooses a particular path. Thus Brown 7 , for example, insisted on using "suggestion" rather than
"association." On the other hand, the physiological bias initiated by Hartl ey9 and particularly
noticeable in Bain 2 and Spencer l6 , often resulted
in associative connections being treated as physical forces or neural links competing in a completely mechanical way. Reading between the lines,
the associationists were apparently torn between
a desire to create a mechanistic, deterministic
theory, resembling contemporary physical and chemical theories, and a desire to preserve the "free
will" of an immanent "soul." (It might be noted
that a theist engaged in artificial intelligence
research today is confronted by a similar dilemma.)
I have been unable to find in the literature
a clear, unambiguous discussion of the selection
problem inherent in any system of competing associations. But this problem cannot be avoided in
the formUlation of our abstract machine. The introduction of a deus ex machina, some free will
demon which selects tokens, would merely beg the
question as to how much might be accomplished by
the relatively simple associationist machinery.
There seem to me to be two main alternatives.
Coupling coefficients might be introduced as transi Hon probabili ties wi th P4 replaced by some rule
governing joint probabilities, in which case the
machine would be heavily biased toward stochastic
processes. The other alternative is exemplified
by the postulates used here, with the machine
biased toward deterministic behavior. This bias
will be magnified by postulates PS and P6 so that
the machine will, in the absence of sensory inputs, tend toward cyclic, stereotyped behavior
patterns with few if any random fluctuations. We
proceed to examine briefly a few behavioral characteristics of the four-postulate machine.
Assume the machine contains just five tokens,
bonded as in Figure 1, and that the attention re~
ister can hold only one token, i. e. , A =1. Suppose
that ml is initially in the attention register.
The sequence of tokens entering A will then be m2,
m4, m2, m4, ••..• , an endlessly repeating cycle.
Let m3 be ini tial1y in A.

r-~ow

the adductioll

fUI1C-

tion for all tokens has the value zero, and the
adduction set F contains all tokens. A token from
F is chosen at random. If M3 is selected, then
the process is repeated until some other token
enters A. The selection of mS will result in m3
returning to A. Eventually ml' m2' or m4 will
enter A, and the endless sequence above will follow.
This example shows two characteristics of the
abstract machine. First, a token that has no
bonds to other tokens, such as m3 (and corresponding to a "terminal node" in graph theory), cannot
stop the machine. It simply provides an equal

THEORETICAL PROBLEMS IN ARTIFICIAL INTELLIGENCE

opportunity for all tokens to enter A. Secondly,
the machine can be easily trapped into cyclic behavior by rings of two (such as m2 and m4), or
more tokens. It should be noted that if the reflexive bond from m4 to m4 had a coupling coefficient greater than 5, it would not succeed itself
since i t s adduction function is zero when it is in A.

to the gener a1 conclusion that the fewer the bonds
between memory tokens, the less important is A .
In terms of association psychology, this conclusion could be characterized by the general rule
that a mind in which ideas are sparsely associated cannot benefit from an increase in attention
span. The behavior of such a mind will tend to
be stereotyped in spite of efforts to increase
the attention span. Certainly the behavior of
the abstract machine becomes independent of A if
memory tokens are organized into simple strings.

Consider the case where A = 2, and let A =
{m1} initially. The sequence of tokens entering
the attention register will be m2, m4, m1, m2,
m4 , ••••• , another endless cycle. No matter which
token, or pair of tokens, is initially in A, the
machine will eventually settle down to this threetoken cycle. This little example demonstrates
that the machine can be trapped into cyclic behavior by networks other than rings, in this case the
chain m1, m2, m4. It is also clear that at least
A+ 1 tokens are required for cyclic sequencing.
Before examining further examples of simple
coupling patterns, it will be convenient to define
"strings," "rings," "chains," and "trees" in terms
of the "predecessor-successor" re1 ation. If cil > 0,
then mi is a "predecessor" of mj and m· is a successor" of mi. A "string" is a group df tokens
containing a unique "origin" token which has no
predecessors and exactly one successor in the
group, a unique "terminal" token having no successors and exactly one predecessor in the group, and
all other tokens in the group having exactly one
predecessor and one successor in the group. A
"ring" is simply a closed string, i.e., a string
without origin or terminal tokens. A "chain," as
the name suggests, has two "end" tokens, each of
which is connected to one token in the group,
which token is both a successor and predecessor;
all other tokens in the chain are connected to exactly two others which are also both successors
and predecessors. Thus two strings are "embedded"
in a chain. A "tree" will be understood to be a
group with one origin token having no predecessors
and two or more successors, several terminal elements having one predecessor and no successors,
and all other tokens in the group having one predecessor and two or more successors. These inelegant definitions will suffice for the rather informal discussions of token strUctures in this
paper.
As a consequence of the adduction function,
all of the tokens in the attention register influence the selection of the next token to be entered into A. This corresponds to the process
Bain 1 called "compound association." Unfortunately, the associationists did not pursue in detail
the implications of such a process. They tended
to think in terms of simple strings and trees of
tokens (using our terminology), and compound
association is not very important in such cases.
Consider, for example, the case where all memory
tokens are organized into a single string and any
one of them is initially in A. Even if A is larg~
once A is filled the adduction function will be
zero for all tokens except the successor of the
last token to enter A. Consequently, the sequencing of tokens through A will correspond to the o~
dering of tokens in the string regardless of the
value of A. Thought experimen ts of thi s so rt lead

However, even simple coupling patterns produce some interesting sequencing phenomena, and
we shall briefly exam~ne a few of these. Let us
first consider the effects of symmetrical bonds,
i.e., cases where c .. =c o. e The four tokens in
Figure 2 are connec%~d ti~ symmetrical bonds having
the indicated strengths. Suppose that A =1 and
that A={m1l initially. The sequence of tokens
through A, which will henceforth be called the A~e~u~nce, is m1 , m2 , m3 , m2.' m3' •••• If A={m3}
1n1t1a11y, the A-sequence w111 be m3' nI , m~, m2'
2
m3 , ••.• Thus we see immediately that symm~tric
bonds do not necessarily lead to symmetric sequences, i.e., m1 , m2 , m3 versus m , m2 , m1 • Fur3
thermore, an increase in A can have marked effects.
Let A =2 and initially A= {ml}' The A-sequence
will be m1 , m , m , m , m , m , m , •••. , a type
2
2
3
4
3
of behavior seen 1n small groups
~ithout symmetric bonds.
In brief, experiments on a variety of small
coupling matrices have failed to show any outstanding effects uniquely correlated with the
presence of symmetric bonds or that such effects
might emerge in large ensembles of memory tokens.
For the sake of simplici ty, symmetric bonds
are assumed in the five-token group of Figure 3,
which illustrates a "hub and spoke" pattern of
coupling (a special type of tree). The bonds between the hub m1 and the outlying tokens have
progressively smaller coupling coefficients. The
effect of increasing A is quite regular for such
a cluster of memory tokens. Let A= {mll initially, and suppose A= 1. The A-sequence will be
m1 , m2 , m1' m2 , .••• For A= 2, the A-sequence is
m1, m2, m3' m1' m2' m3' m1 , .••• ; and for A= 3,
it is m1, m2, m3' m4 , m1, m2' •••• Thus the "hub
and spoke" configuration provides a basic mechanism for cyclic scanning of memory tokens, the
scope of the scanning process being controlled by
A. A simple ring will also produce cyclic scanning, but the scope of scanning cannot be contro~
led by A.
This is an example of sparsely bonded token
clusters which produce marked changes in sequencing as a function of A; it is a counterexample
for the general rule stated above.
Although Gestalt psychology has been a major
opponent of association theory, it turns out that
gestalt phenomena can appear in the abstract machine. Consider the group of memory tokens 1n
Figure 4. Suppose that A = 1 and that ml is in A.

AN ABSTRACT MACHIKE BASED ON CLASSICAL ASSOCIA TIO;\" PSYCHOLOGY

The "response" of the machine is the entry of m2
into A. If m3 is in A, then the response will be
the entry of m into A. However, if A = 2 and
4
~ m and m
are inserted in A, then the immel
2
diate response will be the entry of mS into A.
Thus the machine's response to the joint presentation of ml and m3 in A is quite different from
the "sum" of its responses to ml and m3 presented
separately. This fundamental characteristic of
gestalt processes is therefore obtainable with associationistic mechanisms; there is no necessary
conflict between association theory and gestalt
phenomena. This case will become more significant
after sensory inputs to the attention register are
introduced below.
The length A of the attention register can
influence the sequencing through tree structures.
Consider the simple tree in Figure S. Let A = 1
and A = {mIl initially. The A-sequence will be
ml , m2' m3 , m4 , mS ' m6' •••• For A= 2, the Asequence will be the same; but if A = 3, a new
type of behavior suddenly appears. It might be
called "branch jumping." For A = 3, the Asequence will be ml' m2, m3' m4' mS' m7' m8 , m9 ,
Instead of continuing out the upper branch,
the A-sequence jumps down to the lower branch and
continues on that branch. The crucial factor is
the retention of m3 in A when the weak bond between mS and m6 is reached. At this point, f6 = 1
while f7 = 2; and therefore m7 enters A instead of
m6. Thus if A>l, the A-sequence is not determined simply by the .~elative strengths of coupling
coefficients at branch points in a tree. Clearly,
small changes in A could effect great changes in
the machine's behavior if memory tokens are organized into certain types of trees, another exception to the general rule that Ais an ineffective control parameter for sparsely bonded token
systems.
A case of interest is the basic configuration of "intersecting" strings, i.e., where a memory token is the member of two strings. Two simple strings are embedded in the system of Figure
6, ml through mS and m6 through m9 (including
m3). Of course several other strings can be abstracted from this group, but there is no need to
identify them. Let us assume that all coupling
coefficients have the same value, say, 1.0. Consider first the case where A= 1 and A = {mIl
initially. The adduction set F = {m2' m3 } , and
either token may be chosen to succeed ml in A.
In fact, spt F always contains two tokens: regardless of which token is in A. Thus the machine
operates in a stochastic mode over this group of
tokens, and many A-sequences are possible, e.g.,
ml' m2, m4 , •••• , or ml' m3' m8' m9, •••• If
A = m6 in1tially, the situation is essentially
the same.
Now let A = 2. The behavior of the machine
shifts radically from a purely stochastic to a
purely deterministic mode! Furthermore the intersection of the several strings does not provide
opportunities for "turning corners." To see this,
assume that ini ti all y A = {ml' m2} , with ml the
"oldest" token (it will therefore be ejected

first). The A-sequence is guaranteed to be ml ,
m2, m3' m4 , mS' •••• and on out the horizontal
strings. Similarly, if the machine is moving down
the vertical strings, the A-sequence will be ••••
m6' m7' m3' m8 , m9 , •••• and so on.
The bonds from a token to the next but one
token, e.g., from ml to m~, m2 to m4 , etc., correspond to what are somet1mes called "remote forward associations" in serial learning experiments.
While we will not venture a direct interpretation
of this abstract machine behavior in terms of serial learning, we will adapt the psychological
phraseology to our purposes and refer to these
bonds (in such overlapping string structures) as
"remote forward bonds."
The example above shows that strings accompanied by remote forward bonds may intersect at
many tokens without producing ambiguity in the
sequencing. When A = 2 (or more), it is as if the
sequencing process acquires "inerti a" which carries
it right through intersections without deflection.
Thus a certain economy of memory tokens is possible in the abstract machine; a particular token
may be coupled in numerous strings without destroying the independence of corresponding A-sequences.
This example also shows why it is dangerous
to characterize the machine as either stochastic
or deterministic. Given even this simple coupling
configuration, the small extension of the attention register from A = 1 to A= 2 is sufficient to
shift the machine's behavior from one extreme to
the other. From the standpoint of classical association psychology, this phenomenon is, of
course, very suggestive. The strings with remote
forward bonds might well represent habitual sequences of "thoughts" and "ideas." If, then, the
attention span of an individual is reduced to a
minimum, a condition approached perhaps in "freeassociation" experiments and dreams, the behavior
of the abstract machine suggests that the normal,
habitual thought sequences might be broken up and
replaced by random, novel sequences.
Having examined a few fundamental behavioral
capabilities of the four-postulate machine and engaged in some speculative psychological interpretation, we shall proceed to introduce two more
postulates.
The Six-Postulate Machine
Among the numerous types or "laws" of association that have been proposed there are two that
gained almost universal acceptance. They were
most commonly called "Similarity" and "Contiguity."
The "law of Similarity" may be summarized as the
tendency of ideas or images to become associated
in the mind if they have certain "similari ties" in
quality, structure, function, etc. For example,
the concept of a cat may be succeeded in consciousness by that of a rat because of visual or
auditory similarities in the names. The "law of
Contiguity" draws attention to the fact that ideas
or images which have appeared together or in close
succession in the mind tend to become associated.

THEORETICAL PROBLEMS IN ARTIFICIAL INTELLIGENCE

This principle, translated into a behaviorist
framework, underlies most theories of conditioning.

But nothing further is presumed regarding the
structures of tokens. In particular it should be
noted that these postulates do not imply any transitive relations between internal structures; given
three tokens ml , m2 , m3 and the statement that
bl2 = b 23 , there are no grounds for predicting the
value of b 13 •

Some associationists argued that the law of
Similari ty could be derived from the law of Contiguity, while others argued the opposite. There
were debates concerning the nature of the relation
of "similarity" (germane to the modern problems of
pattern recognition) and so on. See William
James l2 for an excellent critical discussion of
such issues; in this paper they will be generally
avoided. We shall simply postulate two kinds of
bonds suggested by the "laws" of Similarity and
Contiguity, ignore all other types of associative
connection, and examine the consequences.
Postulate PS;

Every coupling coefficient Cij is
the sum of an "external coefficient"
a .. and an "internal coefficient"
~J
.
b ij ; that ~s, Cij = aij +bij for all
m~ and m! in M.
J
~

This is an extension of P2 wherein the bonds
previously discussed are split into two subtypes
which will be called "external bonds" and "internal bonds." As a consequence, the coupling matrix is the sum of an "external" matrix and an
"internal" matrix. This postulate does not require alteration of the definitions of adduction
functions or sets, nor of postulates P3 and P4.
Postulate P6:

Initially, the external coefficient
aij =0 for all mi and m. in M.
Thereafter. whenever bdth m; and
mj appear in the attention ~egiste~
aij is incremented by an amount
oij. The internal coefficient
bij is constant for all time for
all mi and mj in M.

Thus, at "bir th," the machine's ext ernal coefficients are zero; and the internal coefficients have values that will be retained throughout the life of the machine. Initially, Cij = b ij •
Then, if A>l so that two or more memory tokens
may reside simultaneously in the attention register, external coefficients are increased in
value as a function of the particular sequencing
of tokens through the attention register. The
only way to suppress the growth of external bonds
is to maintain A = 1. Otherwise at least one element of the external matrix (aij), and therefore
of the coupling matrix (Cij), will be increased
each At during the lifetime of the machine.
At any time the state of the external matrix
reflects the "experience" of the machine up to
that time, i.e., the past behavior of the machine,
the sequencing of memory tokens through A. The
internal matrix, on the other hand, reflects certain constant relations between the tokens. The
strength of an internal bond, as given by the
corresponding internal coefficient, is intended
to represent the degree of "similarity" in the
internal "structures" of the two tokens involved.
In effect, postulates PS and P6 state that memory
tokens have distinguishable internal structures
and that these struc tures remain forever unchanged.

Although it is tempting to assume that the
relations of similarity, however defined, must be
symuetrical, we leave that an open question here
because a satisfactory discussion would carry us
too far from the main line of development. Thus
it is assumed that bij~b'i is possible. Similarly, postulate P6 does Jot entail the symmetric
growth of external bonds. If mi and m. are both
members of A over a particular time interval, then
both aij and aji will be increased in value. But
it is possible that 0 ij .. 0 3i' The question of
symmetric versus asymmetric growth of external
bonds will be taken up in the discussion below.
Discussion of the Six-Postulate Machine
As more postUlates are introduced, the possible varieties of behavior become ever more numerous and their analysis more difficult. Since
we wish to add several more postulates in this
paper, it will be necessary to hold the discussion
of specific examples to a minimum. In this section two main behavioral issues will be considered.
First, the most apparent effect of PS and P6
is the progressive elimination of stochastic behavior in the abstract machine as time passes.
Consider the fragmentary network of couplings in
Figure 7. Assume that the machine has just been
born so that Cij = bij and the bond coefficients
indicated are therefore equal to the internal coefficients. Let A= 2 and A= {m l , m2} with ml
being the oldest. At this time the adduction set
F = {m3' m4 } because f3 = f4 = 1, and there are no
other more strongly coupled successors of m2' The
next token to enter A will be chosen at random
from F; suppose m4 is selected. After At, m4
enters A and the external coefficients a/.4 and
a42 will be increased by some finite increments.
Suppose that at some later time ml and m2
again appear in A as a result of the coupling pattern for tokens not shown. Now the adduction set
F contains but one member, m4' As a result of
the increase in a24 on the previous pass, f 4> f3;
and there will be no random choice this time. The
A-sequence will again be ml, m2 , m , •••• , and
4
a24 will be incremented again, giving m4 a still
greater advantage over m3 • Thus the selection of
a token to follow m2 into A was initially a stochastic process but has quickly become deterministic. The immediate and obvious conclusion we
draw from this little experiment is that the
growth of external bonds eliminates stochastic behavior that may have been implicit in the initial
coupling matrix.
But suppose that at a still later ti~e m~
and m6 appear in A. If the growth of a24 hasbeen sufficiently small, so that c24 <4, then the

AN ABSTRACT MACHINE BASED ON CLASSICAL ASSOCIATION PSYCHOLOGY

A-sequence will be mS ' m6, m2 , m3 , •••• and a 23
will be increased. A repetition of this sequence
would result in a23 = a 24 and therefore c23 = c24.
Now if ml and m2 again appear in A, f3 = £4 and a
random choice between m3 and m4 is required. Thus
it is clear that the sequencing of memory tokens
in a particular group may be stochastic, then deterministic, then stochastic, and so on indefinitely. A change in A is not required (as in the
four-postulate machine) to shift the machine's
behavior from stochastic to deterministic behavior
or vice versa. The rule that stochastic behavior
is progressively eliminated by the growth of external bonds must hold only for a class of initial
coupling matrices. Unfortunately, I don't know
what criteria define this class of matrices although small-scale experiments indicate that most
simple strings, rings, and trees are members. This
problem is interesting but may not be very important; for when sensory inputs are introduced in
even a rudimentary form, the situation becomes immensely more complicated. For one thing, it becomes both possible and desirable to assume that
initially there are no memory tokens in the machine (and hence no initial coupling matrix), and
that the continuous creation of memory tokens via
sensory inputs produces a growing coupling matrix.

seconds, and therefore a12 is increased by 2 01
and a2l by 2 02' Likewise for a23 and a32. But
ml and m3 will also be co-residents for .o.t seconds
so that a13 will be increased by oland a3l by
o 2. Here we have the creation of remote forward and backward (external) bonds, the former
being stronger than the latter. If X is raised
to larger values, still more remote bonds are
formed.
The coupling pattern illustrated by Figure 6
now assumes a peculiar importance: such strings
of external bonds are the natural result of permitting the machine to operate with X>2, regardless of the initial coupling pattern. Continued
operation of the machine with large,\ 's will simply reinforce these strings because, as demonstrated earlier, under such circumstances the sequencing process acquires a certain "inertia"
which carries it through intersections without deflection. Such strings produce deterministic behavior for A >1 except perhaps at intersections
of the type in Figure 7. Of course predominantly
stochastic sequencing may still be obtained at any
time by setting A = 1, which also terminates further reinforcement of external bonds.

First we note that by P4, memory tokens enter
the attention register one at a time, every ~ t
seconds. Thus the members of A can always be ordered by the times of entry; and given any two
members, one is necessarily "older" than the other.
We have been assuming all along that once the attention register has become filled, the entry of
a new memory token causes the "oldest" token to
be ejected. Now let us postulate that aij is increased by 0 ij every ~t seconds for which both
m· and m. are both in the attention register.
Stmilarl~ for a'i and O··,We also postulate (1)
that if m. is older thanJ~., then Oij > Oji (which
results i~ asymmetric extefnal bonds) and (2) that
the increments 0 i ; and 0 ii are the same for all
pairs of tokens in~the macnine; let's say 01 and
02, respec ti vel y.

Discussion of the six-postulate machine cannot be concluded without a few remarks on the
classical "frequency" and "recency" laws. The
former stated, in effect, that the more frequently
two mental entities appear together in consciousness (for whatever reasons), the stronger the association between them. Thus repetition is a major basis of learning. Clearly, the growth of
external bonds, as postulated in P6, produces such
an effect. The "law of recency" is somewhat more
subtle in its implications. It states that the
more recently two mental entities have appeared
together, the stronger the association between
them. At first glance this "law" appears to require the postulation that associations decay in
strength with the passage of time, in which case
the law would be fundamental rather than derived
from other postulates. However, it is not necessary to postulate decay of associations, at least
in some cases, in order to achieve the effects
described by the recency law. The example of Figure 7 shows that the growth of competing bonds
can, in effect, reduce the strength of a given
bond. The postulation of temporal decay in coupling coefficients remains an interesting possibility and would result in a distinct species of abstract machine. Such machines may exhibit unique
properties, but we will not pursue the question
here.

Consider now three tokens ml' m2' m3 which,
as a result of initial coupling coefficients,
enter the attention register in that order. Case
1: A = 1. Since no two tokens can exist in the
attention register simultaneously, the external
bonds between these tokens are not altered by sequencing through A. Case 2: ,\ = 2. Tokens ml and
m2 will be co-residents for ~t seconds with the
resul t that a12 will be increased by Oland a2l
by 02' Similarly for a23 and a 3 2. Case 3: A= 3.
Now ml and m2 will be co-residents for 2 ~t

In closing, we note that P6 ignores an important issue, namely, the stipulation of limits
on the growth of external coefficients. The associationists certainly assumed that there were
upper limits on the strengths of bonds, limits imposed by the physical properties of the nervous
system. The same assumption is necessary in the
case of any physically realizable machine. If no
temporal decay is present, then eventually all
bonds that are capable of growth would approach
the same strength; and stochastic processes (or

A second behavioral problem of considerable
importance is the general effect of varying X. In
the example of Figure 6 it was seen that "remote
forward bonds" can produce remarkable changes in
behavior as a function of X. As a direct consequence of P6, such bonds (external type) are regularly produced when A> 2.
In order to examine
this effect, it will be useful to introduce some
auxilliary, temporary postulates governing the increment 0 ij in P6.

THEORETICAL PROBLEMS IN ARTIFICIAL INTELLIGENCE

60
some substitute decision agent) would tend to dominate the machine's behavior. At least this is an
obvious theorem. Of course if the growth rate of
coupling coefficients is very small relative to
the upper limits, then this problem might be ignored by assuming that the lifetime of the machine
is too short to permit many coupling coefficients
to reach their limit. However, we will not pursue
the problem here for lack of space, evidence, and
op~n~ons.
We are presently concerned primarily
with the early growth phases of the abstract machine's life, rather than old age and senility
phases.
The Nine-Postulate Machine
For logical reasons we have constructed the
abstract machine from the inside. The six-postulate machine still has no contact with its environment. This is the reverse of the theory construction procedures utilized by the associationists. In developing his epistemology, Locke 13 began with his "tabula rasa" theory which, in opposition to the then popular doctrine of innate
ideas, argued that the mind is initially like a
blank tablet upon which sensory inputs \vrote their
record. The mind gradually forms by accumulations
and interactions of sensations, images, and whatnot derived from sensory inputs. In their theoretical expositions the associationists typically
followed this order of development, beginning with
postulates concerning sensation and concluding
with a description of the mind's internal machinery which ultimately results from sensory inputs.
But this order is not necessary, and I find it
more satisfying to begin with the internal machinery. It is largely a matter of taste, and the development of the abstract machine in this paper
reflects, perhaps, prejudices gained in the computer field where one so often begins with the
central processing units and leaves the question
of inputs and outputs to the last (sometimes with
unfortunate results).
In any event, the next group of postulates
final1y put thp abstract machine in contact with
its environment.
Postulate P7:

There is a sensory register which
at all times contains a set S of ~
sensory tokens sl' s2, s3, •••• s 1/1.

Postulate P8:

At any moment, each sensory token
si in S is bonded to each memory
token m. in A with a strength given
by the Jdiscrimination coefficient"
d .. ; and each sensory token s· in
S~~lso has a "vivacity coeffi~ient"
vi'

Before introducing Tile ninth postulate itwill
be necessary to define a special function and related set. They are similar to the adduction
function and set defined in connection with postulate P4.
For every sensory token si in S there is an
admission function gi whose value is given by

l:
j

d..

( 2)

where j ranges over the subscripts of memory tokens in A. Thus the admission function is the sum
of discrimination coefficients between the sensory
token and all memory tokens in A, added to the
"vivacity" of the sensory token.
The admission set G is defined as follows:
sensory token si is a member of G if, and only if,
there is no other sensory token sk such that gk>gi
and gi > (Js where" (Js" is the admission threshold.
Unlike the adduction set F, the admission set G
may be empty; for the sensory token(s) with the
largest admission function may fail to satisfy the
cri terion imposed by the admission threshold () s.
We are now prepared to state the ninth postulate.
Postulate P9:

Every ~t seconds a sensory token is
chosen at random from the admission
set G (unless G is empty) and entered into the attention register,
causing the oldest memory token in
A to be ejected from the attention
register. As the sensory token enters A, it becomes a memory token
(member of M).

It will be assumed that although sensory and
memory tokens may enter the attention register at
the same rate, namely, one per ~t seconds, these
processes are not in phase. Thus a sensory and a
memory token will never enter A simultaneously,
and there is no need to modify the ejection rules.
It is important to note that nothing has been said
about the nature of sensory tokens or their period
of residence in the sensory register. We will assume that a particular sensory token may enter S
and, if not admitted to A, remain in S for a long
period of time. And if it is admitted to A finally, it may be immediately replaced in S by another
sensory token identical in structure and properties. This represents the presence of a constant
stimulus condition in the environment.
Thus the machine cannot influence the appearance of sensory tokens in S, and its only control
over the ejection of sensory tokens is by way of
admitting them to A where they become memory tokens, i.e., permanent parts of the machine. It is
the environment which determines the nature and
sequencing of sensory tokens in the sensory register; the machine is free only to select, from
those presented, the individuals that will be admitted. If the machine was given motor apparatus
for acting on the environment or reorienting itself relative to the environment, then of course
it would gain some measure of control over the
appearance of sensory tokens in S. There is insufficient space in this paper to introduce an efferent system by formal postulate, but the subject
receives some discussion in the concluding section.
The discrimination coefficients represent
bonds from sensory tokens to memory tokens. Their
values reflect relations between the structures of
tokens, not past experience, and are therefore
similar to the internal coefficients previously

AN ABSTRACT MACHINE BASED ON CLASSICAL ASSOCIATION PSYCHOLOGY

introduced. The discrimination coefficients constitute a first approximation to the effects of a
pattern-recognition process, a measure of the "similari ty" between sensory and memory tokens. Since
the discrimination bonds are presumed to exist
only between sensory tokens in S and memory tokens
in A, a memory token not in A cannot influence the
admission of sensory tokens. Thus the attention
register still has the pivotal role in the ninepostulate machine.
The vivacity coefficients represent an attempt to reproduce the effects of "vivacity" as
postulated by associationists. They assumed that
the vivacity of a sensation or percept is a function of stimulus intensity and other factors, such
as object-field contrasts. Further refinements of
the abstract machine would require postulates governing variables which determine the value of a
vivacity coefficient (stimulus intensity, for example), but in this paper the coefficient will be
treated as a parameter.
At this point in the machine's development we
might well postulate a vivacity coefficient for
each memory token and redefine the adduction function accordingly, for the associationists universally assumed that the objects of memory also had
varying degrees of "vivacity." To be consistent
with the classical theory such a postulate must
eventually be introduced, but again the resulting
complications are too numerous for treatment within the confines of this paper.
The introduction of the admission threshold
provides a distinctly new type of system param~ter comparable in importance to A. Large values of e s will tend to isolate the machine from
its environment, while low values will permit a
steady influx of sensory tokens. If, in further
refinements of the abstract machine, e is converted to a system state variable dete~mined by
events within and without the machine, then there
will be rich opportunities for subtle interactions
between the machine and its environment. Eventually A and ~ (the length of the sensory register)
must also be converted to system-state variables
with similar consequences, as touched upon in the
concluding section.

Discussion of the Nine-Postulate Machine
With the addition of the last three postulatf's we have two "registers." side by side as it
were, with a procession of sensory tokens through
one and memory tokens through the other. Depending upon discrimination and vivacity coefficients,
there may be periodic transfers from S to A so
that the sensory procession may influence the attention procession, but not vice versa. The events
in the abstract machine now represent a crude approximation to the picture of sensory and mental
processes as painted by many associationists. For
example, Spencer l6 imagines himself driving along
the seashore and describes the psychological events
as follows (his "vivid states" correspond to our
sensory tokens, the "faint states" to our memory
tokens): "In broad procession the vivid states--

sounds from the breakers, the wind, the vehicles
behind me; changing patches of colour from the
waves; pressures, odors, and the rest--move on
abreast, unceasing and unbroken, wholly without
regard to ~ything else in my consciousness. Their
independence of the faint states is such that the
procession of these, in whatever way it moves, produces no effect whatever on them. Massed together
by ties of their own, the vivid states slide by
resistlessly. The procession of the faint states,
however, while it has a considerable degree of independence, cannot maintain complete independence.
The vivid states sweeping past always affect it in
a greater or less degree--drag part of it with
them by lateral cohesion."
This rather poetic passage is, incidentally,
a good example of the theoretical statements from
which one must squeeze the postulates for an abstract machine. The associationists assumed quantifiable forces but rarely bothered to quantify
specific parameters and variables.
Spencer's "lateral cohesion" is represented
by the discrimination coefficients in our abstract
machine. Rather than using his ambiguous verb
"drag," we speak of the transition from S to A,
the transfer and conversion of sensory tokens into
A where they can influence succeeding A-sequences.
These transitions correspond to the process of
"copying" in association theory; 1. e., an associationist would call our memory tokens "copies" of
"sensations" or "percepts," although we shall
think here in terms of the physical transfer of
tokens from one register to the other.
The most important consequence of P9 is that
the machine can now "grow." There is no need to
assume the existence of memory tokens at the birth
of the machine. As memory tokens are created, the
coupling matrix expands in size. A newly created
memory token will have no external bonds to or
from other memory tokens, but will immediately begin to form such bonds with whatever other tokens
are in A at the time. Since internal bonds represent inherent relations between memory tokens,
when a token mi is created, b ij and bO i are immediately fixed for all j for all timJ.
What sort of memory token structures will
grow up as a consequence of sensory inputs to the
abstract machine? We shall direct our attention
primarily to this basic problem.
As a first example, consider the fragmentary
network of memory tokens in Figure 8. The tokens
are represented by two kinds of symbols--squares
and circles--to suggest similarities and dissimilarities of token structure, hence the internal
bonds. Suppose that at some time in the past m2
and m4 were created from sensory tokens in that
order. They are dissimilar in nature but were
co-residents of the attention register, and an
external bond has formed between them. We shall
assume in the following discussion that external
bonds are highly asymmetric, i.e., that 8 1 »82,
so that for all practical purposes we can assume
a single external bond from the older to the

younger token. Here m2 was created first, followed by the creation of m4 after ~ t seconds.
Now suppose that at some later time another
sensory token is admitted to A, becoming ml' and
due to a great similarity in structure (detected
perhaps by a pattern-recogni tion system) there are
large internal coefficients for the pair ml' m2 •
As a consequence, m2 gains entry to the attention
register. Let A= 4, and let m3 be created.1t seconds after mI. Now we have ml' m2 , m3 in the attention register. Due to previous co-residence
a24 >0 and due to similarity of structure b34 >0.
Acting together it is likely that m4 will next be
entered into A. Now the attention register contains ml' m2' m3' m • In addition to the internal
4
bonds between ml' m2 and between m3' m4' external
bonds from ml to m3 and m4' and from m2 to m3 will
be formed, while the external bond from ml to m4
is reinforced: and external bonds between ml' m2
and m~, rnA will form to give extra support to the
internal bonds. As a result, the coupling pattern
of Figure 8 will appear.
First we note that if, as we have supposed
above, newly created memory tokens are able to
dominate the selection of memory tokens in the
normal A-sequence, then internal coefficients will
be acting decisively; and there will be a tendency
to form "clusters" of tokens. The pairs ml, m2
and m3' m4 are examples of the simplest possible
clusters. Furthermore, if events in the environment are such that two or more types of memory
token are repeatedly created in a certain order
via the sensory register, e.g., ml followed by m3'
and m2 followed by m4' then strings of clusters
will be created. The coupling within a cluster,
being a combination of both external and internal
bonds, will be stronger than the coupling between
clusters, which we assume will be almost entirely
the result of external bond formation.
A string of clusters might also be viewed as
a bundle of parallel strings with numerous crossbonds. But, in any event, it is clear that the
sort of strings and chains assumed in our analysis
of the more primitive four and six-postulate machines can be created in profusion by sensory inputs. If A is increased well above 4, then remote
forward and backward bonds between new and old
memory tokens will also form. A reduction of A
to, say, A= 2 will result in the creation of only
the simplest sort of string.
If sensory tokens gain entry to A mainly on
account of high vivacity coefficients and are unable to materially influence the normal sequencing of memory tokens, they will be merely "tacked
on" to pre-existing strings by relatively weak
external bonds. Although they have become weakly
coupled satellites of a strong string, they may
at future times provide a basis for formation of
cross bonds, via strong internal coefficients, between widely separated tokens in the main string,
a process that might be called "looping."
Returning to Figure 8, suppose again that the
creation of ml results in the entry of m2 into A,

THEORETICAL PROBLEMS IN ARTIFICIAL INTELLIGENCE

but that the sensory token which became m3 (call
it s3) is this time unable to enter S by reasonof
a high admission threshold. However, the previously formed external bond from m2 to m4 is sufficient, let us assume, to draw m4 into A. We
now have ml' m2' and m4 in A, with s3 sitting in
S. Since s3 is presumed similar in structure to
m4' the discrimination coefficient d 34 is large:
and we will assume that now g3> s and s3 enters
A, becoming m3.

This little example shows an extremely important facet of the machine's behavior stemming
from postulated discrimination coefficients. The
contents of the attention register at any moment
may determine which, if any, of the sensory tokens
will be admitted. The machine need not passively
ingest whatever sensory tokens are presented; rather, under our current postulates, those sensory
tokens which have certain special relations with
memory tokens in A are given an advantage. In
general, the machine will tend to select those
sensory tokens whose nature and order of appearance match the memory tokens concurrently passing
through the attention register. We might say that
the machine "pays attention" to some sensory inputs and "ignores" others, depending upon the state
of the machine at the time. By now it should be
abundantly clear why the attention register is so
named. Of course this selectivety may be abolished at any moment by the appearance of sensory tokens with high vivacity coefficients and/or a
marked decrease in the system parameter
s• A
very vivacious sensory token can "force itself"
upon the machine and, by way of internal bonds,
disrupt the current A-sequence and initiate a
distinctly different series.

It should be noted that if A is large, say,
A> 5, then i t will be less likely that sensory
tokens disrupt the normal sequencing of memory
tokens unless the machine's memory tokens are
sparsely bonded into simple strings with few remote forward or backward bonds. A very youthful
machine will, in fact, tend to have only sparsely
bonded strings and hence will be strongly influenced by sensory inputs even if A is large. But
as the machine grows older and the memory tokens
become densely bonded, it will be decreasingly influenced by its environment; indeed whenever A is
reasonably large, an old machine will tend to select only those sensory inputs which fit in with
its experience (internal and environmental). Thus
it appears that as the machine grows older it will
display a type of rigidity in its behavior (relative to the environment) which is quite distinct
from the tendency to deterministic sequencing discussed earlier.
In Figure 9 we suppose that at some time in
the past m2 and m4 were created in sequence and
are externally bonded. Now ml is created and due
to a strong internal bond draws m into A. But
2
the creation of ml is followed by the creation of
m3' which is quite different from m4 . An external
bond is formed from ffi2 to m3' and it may be as
strong as the old bond from m2 to m4. We have in
this process a basic mechanism for the creation of

AN ABSTRACT MACHINE BASED ON CLASSICAL ASSOCIATION PSYCHOLOGY

"tree" structures in the coupling matrix. If in
the future m2 enters A, then there may follow a
random choice between m3 and m4 unless, of course,
a sensory token is meanwhile admitted and turns
out to have a strong internal bond with m3 or m4'
thereby determining the A-sequence. On the other
hand if, say, c24> c23' the A-sequence is deterministic unless a sensory token is meanwhile admitted and creates a memory token with a strong
internal bond to m3 • It may be then that f3=f4'
and the A-sequence becomes stochastic rather than
deterministic.
In brief, it is clear that not only can tree
patterns of coupling be easily produced, but that
further sensory inputs may either cause or prevent
stochastic sequencing in such tree patterns. Having shown how branches are formed, the equally important formation of merging strings must be demonstrated.
Consider Figure 10. At some time in the
past, m2 and m4 were created in sequence and are
accordingly bonded externally. At a later time,
ml is created, followed by the creation of m3'
which has a strong internal bond to m4 .Assuming
A > 2 and that m3 causes m4 to enter A,an external bond from ml to m4 is formed. Hence m4 becomes a point at which strings merge. In the future, both ml and m may be followed by the same
2
token, m4"
SJnce the machine can produce strings,
branching strings, and merging strings, it appears
that any conceivable finite coupling matrix can
also be created given appropriate sensory inputs
in the past. But this is not a proven theorem.
It is an extremely important theorem because, if
true, then whenever one finds a coupling matrix
which produces a desirable or interesting behavior
pattern (with or without further sensory inputs
assumed), it is guaranteed that there exists at
least one possible history of the machine which
would lead to the coupling matrix in question.
My intuition tells me that the theo~em must be
true, but it also seems quite likely that new behavioral principles will emerge if machines with
large numbers of memory tokens (say 100,000) can
be examined in detail. It is conceivable that
really large token ensembles, given the postulates
introduced here, have a class of "forbidden"
states, i.e., forbidden coupling matrices. I have
no proof, and of course the classical associationists never pursued their theory in sufficient detail to even recognize tllC:~ existeru:.e of this problem.
A less serious problem arises from the likely
formation of clusters of memory tokens connected
by strong internal bonds (as in the first example
above, Figure 8). It appears that if the number
of tokens in a cluster exceeds A, the machine
would tend to be trapped, to cycle endlessly within the cluster. This is another problem not recognized by the associationists. It would be
desirable to have just one or two tokens from a
cluster enter A, "stand for" the whole cluster as
it were, and then have the A-sequence move on to

the next cluster. This seems to have been assumed
by the associationists; but it is clear, within
the framework of our present machine, that a special kind of postulate must be added in order to
produce the desired behavior. It will be touched
upon in the concluding section.
There are numerous other effects, such as
conditioning and gestalt responses, which can be
demonstrated, at least in a rudimentary form, to
be possible in the nine-postulate machine. Some
of these were discussed briefly in connection with
the behavior of the four- and six-postulate machines and can be easily extended to the nine-postulate case.
To summarize, the introduction of sensory inputs in even the crude form of P7, P8, and P9
yields a machine which grows with the passage of
time. It is not "preprogrammed" in the usual
sense, having just two "registers," the ability to
create permanent memory tokens from transient sensory inputs, and two kinds of coupling between tokens --- one that suggests physical links (external bonds) and one that suggests the existence of
a pattern-recognition apparatus or "resonance"
phenomenon (internal bonds). The coupling patterns
which grow within the machine reflect the pattern
of events in the environment. As the machine grows
older, these patterns may become self-reinforcing
by selecting from the sensory input only those tokens which match themselves. This tendency may be
disrupted by the appearance of sensory tokens with
relatively large vivacity coefficients (e.g., due
to strong stimuli) or by a drastic reduction in
the length of the attention register (in psychological terms, a state approximating that achieved
in "free association").
If the sequencing of memory tokens into the
attention register proceeds at a somewhat faster
rate than the admission of sensory tokens, it will,
in effect, be continually "predicting" future
events in the environment on the basis of past experience. By this I mean that a sequence of the
sort obtainable from the group in Figure 8, for
example, can lead to a prediction: the A-sequence
ml' m2 can bring in m4' which is a "prediction" of
the type of sensory token that will appear in S.
But of course the machine has the nasty tendency
to select for admission those sensory tokens which
satisfy its own predictions --- a habit not entirely unknown in humans and perhaps exemplified
by this paper.
Conclusion and Glimpses of Further Postulates
It must be emphasized that the nine-postulate
machine constitutes neither a complete nor unique
interpretation of classical association psychology. The vagueness of the associationists' doctrine and the variations from one author to the
next suggest a variety of interpretations •. We have
presented here but one partial interpretation.
The analysis of the abstract machine's behavior has been based on small groups of tokens.
However, the association theories were intended to

explain the behavior of the human mind, a very
large collection of objects to say the least. The
major problem posed by the abstract machine is,
similarly, its behavior when large numbers ofmemory tokens --- say 10 5 to 10 7 --- have been accumulated and are interacting with each other and
with environmental inputs and outputs. Sma11group analysis can at best suggest general conclusions regarding large group effects, and the arguments in this paper are only tentative. We are in
dire need of techniques for analyzing massive collections of tokens.
From the standpoint of artificial intelligence, the most interesting aspect of association
theory is its purported ability to account for the
growth of mechanisms that can "think," a growth
that begins with nothing more than a few forces
operating on the products of sensory inputs --Locke! s "tabula rasa" concept. If the associationists! claims are accurate, then they have, in
fact, invented a machine which structures itself
without the aid of "pregrogramming." But their
claims have never been confirmed experimentally
(in humans) nor have the logical consequences of
their axioms been explored in any detail. Abstract
machines of the sort discussed here provide a vehicle for such explorations providing that sufficiently powerful analytical techniques can also be
evolved.
Computer simulation seemS to offer, at present, the most promising approach to analyzing the
abstract machine, although mathematical analysis
has not yet been given a fair testing. Whether
or not the complex combinatorial problems, which
arise when a reasonably complete machine has
grown beyond several hundred tokens, can be successfully attacked by conventional mathematical
techniques remains an open question awaiting the
attention of suitably talented mathematicians.
However, the abstract machine has been constructed
in such a way that it can be simulated ---though
the cost might be forbidding --- on a genera1purpose digital computer.
In constructing the abstract machine, the
most difficult decision is confronted in formulating a mechanism for choosing among tokens which
have equal claims to succession. This problem is
inherent in any quantified associationa1 system
where objects are competing for attention. The
associationists never faced this problem directly,
preferring to leave a certain loophole through
which a free-will soul might be slipped should the
theory threaten to become ~ successful.
We have here postulated a selection mechanism which utilizes random choices only when two
or more tokens have exactly equal claims on the
machine's attention. Such random selections are
presumably based on some "noise" mechanism. Depending upon assumptions regarding the growth of
the co~pling matrix, random selections mayor may
not be frequently required. We have shown by example how stochastic processes appear or disappear as a function of coupling patterns and variations in A. I believe this is one of the most

THEORETICAL PROBLEMS IN ARTIFICIAL INTELLIGENCE

interesting aspects of the association problem.
Of course there are promising alternative mechanisms, e.g., a machine in which coupling coefficients are treated as transition probabilities; but
space is insufficient to discuss them adequately
so they have been ignored altogether.
The forces operating in the machine, as represented primarily by external, internal, and discrimination coefficients, are few but by no means
simple in their physical implications. They have
been assumed without regard to the difficulty of
physically realizing them in any real machine
(although, again, they can be simulated by brute
force methods). The objective is to explore the
logical consequences and promise --- if any --- of
associationa1 mechanisms, If they are sufficiently promising, attention can then be directed to
the problems of physical realization.
The results of research to date, only part of
which is reported here, is inadequate for any firm
conclusions as to the ultimate capabilities of the
abstract machine. That the machine is capable of
"learning" in at least several senses is obvious,
although we have avoided the use of that term.
The machine does produce an internal "image" or
"model" of both regularities and irregularities
in the external world, and this internal structure
can clearly be used to predict the future in a
rudimentary way. Assumptions regarding the possible species of memory and sensory tokens have
been avoided but remain a complex problem of great
importance that must be bypassed in this introductory paper, As noted in the introduction, the aim
of this paper is to be suggestive rather than definitive, a necessity in view of the limited data
in hand and restricted space available.
The nine-postulate machine falls so far short
of the implications of association theory that it
would be misleading to conclude without a few
brief remarks on other postulates that should be
and are under investigation.
First, a group of postulates creating amotor
apparatus is required. An "efferent register"
containing a set E of tokens seems the most direct
approach. We distinguish two species of memory
tokens: those that can be entered into E and
those that cannot. In order to deal with the most
primitive types of reflex behavior, it may be desirable to permit the direct transfer of sensory
tokens from S to E. In any event, the set E causes
the machine to act on its environment in specified
ways. This makes it possible to consider the dynamics of feedbacks through the environment to the
sensory register. In particular, the machine is
then capable of focusing on some part of the environment and thereby stabilizing certain subsets
of S. More import~~tly, it must be postulated
that the scope of S can be expanded or contracted,
relative to a sensory manifold, by the members of
E.
Second, the sensory register must be broken
into several parts representing different sensory
modes, and coupling coefficients between sensory

AN ABSTRACT MACHINE BASED ON CLASSICAL ASSOCIATION PSYCHOLOGY

tokens within a mode be introduced. These coefficients should be partially responsible for determining vivacity coefficients, and for admission
functions connected with the multilevel attention
register discussed below.

a brief period, then finally its ejection. Transition c is forbidden by postulate. Set d shows
how a token may move among the various attention
registers for a considerable period of time before
ejection.

Third, all memory tokens must be assigned vivacity coefficients whose values are functions of
those accompanying the sensory tokens from which
these tokens were created. The adduction function
must be appropriately redefined.

As suggested by Bain, the increment in external bonds between co-residents within any given
attention register is an increasing function of
the level of that register. Thus external coefficients for co-residents in A2 would increase at a
greater rate than those for co-residents in A1'
Clearly multilevel attention registers create rich
opportunities for multiple sequencing and the formation of complex coupling patterns.

Fourth, an entirely new type of coupling must
be introduced. In this paper we have considered
only token-token coupling, but token-system coupling is required to represent the influence of
general "system states" upon the machine's behavior. For example, we postulate a system state
parameter P which ranges between positive and negative limits: call it the "Pleasure-Pain" scale.
When memory token m1 is created, its p1easurepain coefficient P1 is set equal to the current
value of p. The adduction function is redefined
to f.
I c. . + PPi When P and Pi are of
l.
j
Jl.
the same sign and relatively large, the state of
the system as a whole can be responsible for the
selection of m· for entry into A. The next step
is to convert ~ to a state variable whose value
is determined, partially at least, by certain
sensory tokens. Further refinements to this token-system coupling scheme carry one well beyond
the classical theory.
Fifth, several levels of attention registers
must be postulated. As Bain 3 put it in a poetic
outburst: "No associating link can be forged ••••
except in the fire of consciousness; and the rapidity of the operation depends on the intensity
of the glow." He was referring here only to those
types of bond which can be reinforced; in our
machine, external bonds. It was generally recognized that there are degrees of consciousness,
and we interpret this as discrete attention registers. Let us say that there are n attention
registers of lengths A1 , A2 , •• An which hold sets
A1, A2, ••• An. Each attention register is assigned a "level coefficient" k wi th k1 1, is a
rule of inference of L and W l' W2' • . ., W r
are words of L, we will say W1 is a consequence
in L of W , • • . ,W (by rule of inference R.)
2 ~----~---~
I
whenever Ri(W l' W2' . . • , Wr) is true. Then
the formal definition of a proof in L is given as
follows: A finite non empty sequence of words
W l' W2' . . ., Wn of L is a proof in L of a
word W if and only if W

= Wand for each

n, either

Theorem 1 The set of theorems of an axiomatic
language L is recursively enumerable. 6

This means, of course, that the theorems of L
can be produced by a program.
Finally, the language L is assumed to be
arithmetical, in that any sentence in ordinary
arithmetic, using the symbols '+', ,. f , ' = "
and parentheses, numerals, variables, and
quantifiers, has- a formal counterpart in the language L; also, whenever one is able to prove both
A, and A implies B, then one is able to prove
B . Under these conditions, we give the language
the standard interpretation over the integers, and
regard a statement of L as true, if and only if its
interpretation represents a true property of the
integers. One further requirement on L is that
every function f(x , . . ., x ) computed by a
1
n
program be representable in L, where by 'representable' we mean that if F(X , . . ., Xn) is
1
the formal expression in L whose interpretation is
f(x , . . ., x ), then one may formally prove in
1
n
L either F(a , . . ., an) = y or its negation,
1
according as f(a , . . ., an) = y or not.
1
Now it may happen that-there is some formula
f(x) in L with the property that one can prove in L
that f(x) -f
although each substitution instance
of x = 0, 1, 2, . . . in f(x) = 0 is provable.
That is, it is possible to prove each of f(O) = 0,
f(l) = 0, f(2) = 0, . . ., and f(x) -f O. In
this event, L is called ~- -inconsistent. Evidently,
-O)--inconsistent arithmetical languages are unsuitable formalizations for arithmetic.

We are now able to state the famous theorem
of Godel referred to above.
Theorem 2 (Godel's Incompleteness Theorem)
Either the formal axiomatic arithmetic language
L is 0) -inconsistent, or the set of its true sentences is productive.

(i) W. is an axiom, or
1

(2) There are j l' . . ., jk all less than i,
such that W. is a consequence in L of W. , . . .,
1

W. by one of the rules of inference of L.
Jk
A Theorem is a word for which there is a
proof. Then we have:

Notice that Godel's incompleteness theorem says
that the system L is either unsuitable for arithmetiC, or, there exist true sentences that are
forever unprovable, and that we are able to write
a program which can produce the unprovable true
sentences in question!
You may wonder why this presents any difficulty, since if one can effectively produce a

THEORETICAL PROBLEMS IN ARTIFICIAL INTELLIGENCE

sentence which is true and yet unprovable one is
able to add it to the set of axioms, and, a fortiori,
it is provable! The negation of this procedure is
given by the following observation.
By Theorem 1, the set of theorems or provable sentences of L is recursively enumerable.
On the other hand the set of true sentences is
productive and hence not recursively enumerable.
It follows that the set of true sentences can never
coincide with the set of provable sentences I
The connection between this result and the
problem of simulating creative intelligence on
machines can now be made. Briefly, it is this:
The operation of each large scale digital computer can be represented in a formal arithmetic
axiomatic language since in supplying answers
to problems it proceeds in a step by step manner
in response to built-in directives which may be
regarded as rules of inference. Since these machines are suitable for arithmetic, the representing language may be assumed to be (J) -consistent. Thus there exists an infinitude of true
sentences which are forever inacessible to the
machine. This is regarded in some quarters as
implying the impossibility of ever employing machines as creative robots to aSSist man in his
mathematical chores in more than a trivial capacity since all machines employed in such tasks
are assumed to be susceptible to this argument.
Let us remark first of all, that Godel's
theorem does not say that the true sentences produced by the productive program are unprovable
by any conceivable means, but rather, that they
are unprovable by the specific means already
formalized within the language. That is, once
all the methods of proof to be available are
formalized within the language, or, equivalently,
once the deductive system the language represents can be regarded as closed with respect to
proof methods, then inaccessible true sentences
arise. Of course, no one has ever exhibited a
programmable proof procedure which is not
formalizable in a language such as we have been
considering. It is a fact however, that Godel's
theorem does not inhibit the possibility of the
existence of such a proof procedure, 'and so until
all the precincts have reported in, there is just no
reason to prejudge the question. 8 Which leads us to

set of true sentences of an (J) -consistent language L.
The answer to this question was given in a remarkable theorem by deLeeuw, Moore, Shannon
and Shapiro, and is 'yes'. We will attempt to
sketch this result within the framework of the
definitions and results in Part 1. But first let us
preface some heuristic remarks.
Of course every finite set of integers is recursively enumerable. One has for this case,
the program

1. WRITE A1
2. WRITE A2

n WRITE A

On the otherhand, 'program' means '·finite
list of instructions', so given an infinite nonrecursively enumerable set
A = a ,a ,a ,
1 2 3
. . . , an' . . . simply storing a. in B. for
1

and listing the infinite sequence

i = 1,2,3, . . .

of instructions
1. WRITE Bl
2. WRITE B2

n. WRITE B

Part II
In this part we will conSider the following
question: Can the concept of 'program' be modified so as to retain as much as possible of the
old formulation, and somehow permit the generation of sets which formerly were not recursively
enumerable? Naturally, for a particular nonrecursively enumerable set, we have in mind the

will not result in a program.
Next, suppose we construct a program conSisting of simply
1. WRITE B

THE GODEL INCOMPLETENESS THEOREM AND INTELLIGENT MACHINES

and then successively store a.,
1

i = 1, 2,3,

· . . in B. It is clear, that in a finite amount
of time we can output each member of A. Have
we recursively enumerated A? The answer to
this question is obtained by recalling the definition of recursive enumerability. We see that the
definition requires the program to output the set
and only the set. The program above will output
anything stored in B. We suspect that we shall
have to look somewhere between the two extreme
methods for enumerating A we have given above,
and that the method we seek will somehow be concerned with some nonfinite concept.
We consider now, programs possessing a
countably infinite number of fixed storage locations AI' A , A , . . . such that each Ai can
2
3
contain either 0 or 1. We will call such a program a concatenating program (CP) if for each
n = 0, 1, 2, 3, . . ., and each n-tuple of
0' s and l's (aI' a 2, . . ., an)' stored in AI'
· . ., A the program writes a finite sequence

CP :
2

1. WRITE Al

CP :
3

1. B=B+1
2. WRITE B
3. WRITE ~
4.

CP :
4

GO TO 1

1. C = 2'B

(we assume a subprogram for multiplication is available)

WRITE C

3. B=B+l
4. GO TO 1
For the above programs 1-4, we have the following functions 1-4 computed

of integers f(A , . . ., A ) =
1
n

(n., n. ,
Jl)2
· . ., n. ) such that f(A , . . . A ) is an initial
1
Jr
m
segment of f(A 1, . . ., Am +n ) if (aI' . . ., am)

is an initial segment of (aI' . . ., a

m+n

n times

=(1, 1, 1, . . ., 1 )

). When

A = (an' . . ., an' . . .) is an infinite se-

quence, f(A , . . ., An" . .) is the sequence
1
of symbols consisting of all the initia~ segments
f(A , . . ., An)'
1
From an intuitive point of view, a CP operates as follows: It sees the contents of Al and
writes f(A ) and halts. Then it sees the contents
1
of A2 and writes f(A ) immediately after f(A )
2
1
obtaining thereby f(A , A ) and halts, and so on.
1 2
Let's give some examples of CP's. Here B, C
1= A. for any i = 1, 2, . . .
1

. . .,

(n, A ) )
n

(0,2,4, . . .,
2(n - 1) )
Note that the sets of integers written by programs
1-4 are respectively the following:

2. IF (~) 3, 4

4. WRITE

5. GO TO 1

CP 3:

The set of all ordered pairs (n, An)

CP 4:

The set of even integers,

and that with the exception of CP3, all programs
are oblivious to A. for all i.
1

THEORETICAL PROBLEMS IN ARTIFICIAL INTELLIGENCE

Given a sequence A = (a , a 2 , . . ., an'
1
. ) and a CP with a. stored in A. for i
1

= 1, 2, . . ., n, . . ., we say the set of integers written by the program is A-enumerable.
It can be shown that when a. = 1 for all i, any
1

A-enumerable set is recursively enumerable.

Consider now, any real number 0 < p < 1.
-1
If we expand p as a binary decimal p = a l' 2 +
n
1-.
a · 2- 2 + • . . + a .2+ . • . , ,wuere
ai
n
2
= 0 or 1 for all i, we may associate with p, the
infinite sequence Ap = a 1 , a 2, a 3 , . . ., an'

. . . where the a.' s are the coefficients in the
1

expansion. The result proven by deLeeuw,
Moore, Shannon and Shapiro is

program, the problems involved are extremely
difficult, perhaps impossible (for reasons as yet
unknown). It is clear, however, that the concept
of concatenating programs enhances the possibility of the emergence of computing machinery
from its current chrysalis to a higher species of
resourcefulness.
Apropos the possibility of actually building
concatenating programs, let us remark that
deLeeuw, Moore, Shannon and Shapiro have shown
that A -enumerability is equivalent to being enup
me rated by a program which is equipped with a
device which stores 0' sand l' s in some specified
location at discrete intervals of time t = 0, 1, 2,
. . . with probability p, 0 < p < 1 of storing 1
and probability 1-p of storing zero, each storing
being a.11 independent event. The program then
runs as usual. We see no reason why this kind of
machine can not be built. Of course the problems
of producing the correct program to link the device to still perSists, but we are still hopeful.
A bon chat, bon rat.

Theorem 3 Let 0 < p < 1, and let Ap

References

. . . , an' . . be as above.
Then if there is a program P which computes a
function f(B) such that f(B) = a for all B, then
B
every A -enumerable set is recursively enup
merable: otherwise there are A -enumerable
p
sets which are not recursively enumerable.

~
-i
The numbers p = i=1 a i 2
having the
property that there is a program which computes
the coefficients a. are called computable. It is

Davis, M., Computability and Unsolvability,
McGraw-Hill, 1958.

Kleene, S. C., Introduction to Metamathematics, Van Nostrand, 1952.

deLeeuw, K., Mo::>re, E. F., Shannon, C. E.,
and Shapiro, N., "Computability by Probabalistic Machines", Automata Studies, ed.
Shannon and McCarthy, Princeton, 1956.

Nagel, E., and Newman, J. R., Godel's Proof,
New York University Press, 1958.

Myhill, 'John, Lecture Notes, Univ. of Mich.
Eng'g. Summer Conference, 1961.

Fraenkel, A. A., and Bar- Hillel, Y.,
Foundations of Set Theory, North-Holland,
Amsterdam, 1958.

known that almost all (in the sense of the Lebesque
theory) real numbers
0 ~ x ~ 1 are not computable. That is, the probability of picking such
a noncomputable real number at random is 1. 9
The answer to the question raised at the beginning of Part II "can programs be modified so
as to obtain recursively nonenumerable sets" has
been answered affirmatively. What does this
bode for the prospects of developing creatively
intelligent machines? We think it offers much
encouragement in that it assures us that some
sets of integers formally thought to be inaccessible to machines, may now be obtainable via
some concatenating program. Of course we do
not know at this juncture whether the nonrecursively enumerable set of true sentences of
arithmetic can ever be Ap-enumerated by some

Notes

Our use of "intelligent" with respect to machines refers to their performing of tasks
such as the deciding of mathematical problems, and does not necessarily coincide with
any other current usage of the word. \lIe note
that many mathematicians believe machines
may ultimately contribute solutions to nontrivial problems. For example, Tarski's
deciSion procedure for elementary algebra
and geometry is regarded by Fraenkel and
Bar-Hillel [6] as a method of great potential
in this respect.

THE CODEL INCOMPLETENESS THEOREM AND INTELLIGENT MACHINES

Notes (Cont)

P M(\) is an element of M that fails to be

Judging from discussion at the recent AMS
Convention neither does Professor Marvin
Minsky.

This method was first used, as far as we
know, by Professor John Myhill [5] .

Instruction #6 is simply: IF A 1, 1.

Because of the convention that the empty set
(of integers) is recursively enumerable, we
require a productive set to nonempty. The
precise connection between the productive
program PM of a productive set M and any
program P enumerating a subset of M is
given by means of the so called Post
enumeration of programs which defines an
injection (1-1 map) of the set of programs
into the integers. Thus if the set of enumeratedprograms is P. , P. , P. , . . . , the
11

exact relationship is then, whenever P.
~
enumerates a subset of a productive set M,

enumerated by P. . This property provides
~
an additional argument for the assertion
that a productive set is never recursively
enumerable, for if a productive set M were
recursively enumerated by some program
P. in the Post enumeration, then P M(~)
~
would be an element of M which fails to be
enumerated, which is absurd. See Davis
[1] , Sect. 5.4 and Theorem 5.1.4.
6.

See Davis [1] , Theorem 8.1.1.

See Kleene [2] , p 204 ff, and Davis [1] ,
Theorem 8. 3. 7.

See chap. VIII of Nagel and Newman [4] for
discussion and commentary.

This is, of course, mathematical probability
only; so far as we know there is no practical
procedure for producing these numbers by,
say, machines.

A SUPERCONDUCTIVE ASSOCIATIVE MEMORY

Paul M. Davies
Abacus, Inc.
Santa Monica, California
Consultant to Space Technology Laboratories Inc.
Redondo Beach, California

The general properties of an associative
memory are explained, and their advantages relative to a random access memory discussed.
Then, a superconductive mechanization of such
a memory is described which is based upon the
cross fiJ.m cryotron. The memory requires 5
cryotrons per bit and 9 cryotrons for a control.
module associated with each word. Any combination of bits of the word can be used as the key,
and any number of records in the memory can be
identified and read out as the result of a
single association. The speed of various
circui ts in the memory is approximated and some
applications are suggested.
Introduction
Within the last year, considerable
attention has been focused upon a new memory
organization which possesses certain properties
which make it more powerful in many applications
than the random access memory. This memory is
called the associative memory because of its
ability to retrieve records from storage on the
basis of an association between a key transmitted
simultaneously to all words of the memory and
selected data portions of the stored records. l
A more complete definition of the type of
memories I shall discuss would prescribe the
following properties:
1. A record is written into memory wi thout the specification of an address. The record
is transmitted to all memory words and stored
in the first empty one.

2. A set of records in the memory can be
tagged as the result of en association between
a set of bits called a key transmitted to all
memory words and the corresponding bits of the
stored records. In the memory to be discussed,
there are no restrictions on the set of bits of
the record chosen as the key. There is also no
restriction on the number of records which can
be tagged by a single association. In general,
the association can be any relationship between
two numbers: equality, less than, greater than.

However, in this talk, only equality association
will be discussed.

3. Records which have been tagged as the
result of an association can be read from the
memory one at a time.

4. Tagged records can also be cleared
from the memory.
Organizational Advantages
Before proceeding to the description of
mechanization, I should like to address myself
to two preliminary questions. First, "What
are the advantages of the associative memory
organization?"
Consider the problem of maintaining vehicle
registration records. 8'llppose that each record
contains the owner's name and address, the
license number, and the engine number. Assuming
that a random access memory of large enough
capacity were available to store such a file,
there would still be considerable problems in
organizing the file and retrieving required
records from it. In the first place, there is
no simple way to relate any item of the record
to a memory address. This is because of the
redundancy of the items. For example, if the
maximum length of
owner's name is 20 letters,
then there are 26 2 possible names. Obviously,
it is impractical to have a memory with that
many words so that the names can not be used
to address the words directly. Similar conclusions are drawn from a consideration of the
other items of the record.

If the records a.re stored in the memory
at random, then a sequential search must be
made through half the memory ,vords, on the
average, to find a desired record. This
situation can be improved by maintaining the
file in a sorted order. In that case, a record
could be located in approximately log2 N lookups where N is the number of records in the file.
Thus, 10 look-ups would be required to pick
one record out of a thousand. This could be

DIGITAL STORAGE AND CIRCUITS

done as follows: If there are N words in the
memory, first read word N/2. A comparison of
its key with the one being sought will indicate
whether the desired record is in the first or
second half of the memory. Next, read record
N/4 or 3N/4 according to the previous decision,
and so forth.
It is true that such a method would
greatly reduce the number of look-ups. However,
it has many disadvantages. First, the file
must be maintained in a sorted sequence. Therefore, every time a record is to be added to or
de~eted from the file, a word must be made
available or closed up at the proper spot. This
requires re-recording about half the records in
the memory. Secondly, it is often desirable to
look-up records on the basis of different keys
at different times. In the case of the vehicle
registration records, any of the i terns listed
above might be used as such a key. But, the
memory can only be sorted on the basis of one
key. Therefore, several files would have to be
maintained. Finally, additional time and. logic
are required to perform the process described.

An associative memory solves all of these
problems. Each record is stored only once and
no particular ordering of the records is
maintained. When a record is to be retrieved,
an appropriate key is transmitted to all memory
,vards. This may be the man I s name, the license
number, etc. Simultaneous comparisons are made
in all words to find matching keys and the
selected record or records are read out. Any
combination of.bits of the record may be used
as the key and this combination may be changed
from one retrieval to the next. For instance,
the license number may be used for one search
and the engine number for the next. It is also
possible to use the owner's last name and the
first three digits of the license number.
Furthermore, if more than one record responds
to an interrogation, all responding records
may be read out, one at a time. There is no
limit on the number of records that may be read
out in this way. Numerous applications of these
techniques suggest themselves in such areas as
the analysis of military intelligence.
Another important characteristic of the
associative memory is the manner in which
records are stored in it. Since an address
need not be specified to store a record, it is
not necessary to keep track, externally, of
which words are empty and which are full. This
avoids the, sometimes unpleasant, alternatives
available with a random access memory of either
searching for an empty word or keeping track of
the empty words by means of a program, an
additional list or a special ~-rangement of the
data in the memory.

The Suitability of Cryotron Mechanization
The second preliminary question I should
like to consider is, "Hhy use cryotrons?" They
are not the only possible means for mechanizing
an associative memory. tlowever, "tney possess
the following desirable attributes:
2
1. They are small. Densities of 100/ in
leaving room for interconnecting wires can be
achieved at present, with much higher densities
forecast.
2. They consume little power. This is
important since a basic requirement of the
associative memory is that logic be performed
simultaneously in all words. Present cryotrons
consume as little as 2 x 10-6 watts of power
when switching at maximum speed. This is
sufficiently low that present cryostats can
handle the power dissipated by presently
planned memories. Furthermore, as the circuits
are made smaller, and more numerous, the power
per bit goesdo}VIl§.§_ the square of the linear
scale so as to exactly compensate for the increase in number of circuits. Therefore, a
densely packed plane of microscopic circuits
should dissipate no more heat than present
configurations.

3. The cryotron provides logical
functions as well as memory functions. Furthermore, the output characteristics are compatible
wi th the input requirements so that memory
devices and logical devices ean communicate
with each other with no buffering.
4. Cryotrons do not impose severe
power requirements on external drive circuits
nor severe gain requirements on output circuits.
In addition, these requirements are not
particularly increased by increasing the size
of the memory.
The structure in General
Figure 1 is a block diagram of an
associative memory. The memory consists of a
cXJ~genic data block which communicates in
parallel with a transistorized M register. The
data block consists of m words of n bits each.
Each word consists of a control module which
controls writing, comparing and reading in that
word and a data module which stores one record
or word of data. The M register which is outside the cryostat is similarly composed of a
data module and a control module which communicate with the data block by means of lines
entering the cryostat. In the diagram, the
data lines vertically connect each bit of the
~1 register with the corresponding bits of all
the memory words. Similarly, the control module

A SUPERCONDUCTIVE ASSOCIATIVE MEMORY

of the M register is connected by vertical lines
to all control modules of the data block.
To store a record in the mem.OI"J, the record is placed in the M register. It is then
transmitted simultaneously to all memory words
along the vertical data lines. At the same
time, control signals on the vertical control
lines select the first empty word counting
from the M register. In response, the control
module of the first available word sends a
signal along a horizontal line joining all data
D~~S OI ~~s word.
Tnis causes the transmitted
data bits to be recorded in the selected word.
Ordinarily, one of the transmitted bits is a
t'busi' indicator which identifies the word as
being occupied so that later data will be
stored elsewhere.
To select a record or set of records to
be read or erased from the memory, a key which
identifies the desired records is placed in the
M register. There are no restrictions on the
choice of this key. It may consist of any set
of bits of the record whether they be contiguous
or not. However, ordinarily, one of the bits
will be the "busy" indicator so that only busy
words will be interrogated.

The key is transmitted simultaneously to
all memory words along with certain "enabling"
signals that indicate which bits constitute the
key. The other bits are ignored in the comparison process which follows. At the same time,
control signals are sent to all control modules.
In each word of the data block, a comparison is
performed between the transmitted key bits and
the corresponding stored key bits. Wherever
the two compare, this fact is recorded in the
associated control module. In this way, all
records in the memory which are identified by
the transmitted key are tagged for future readout or erasure.
To read a set of records which have been
tagged in this way, read control signals are
sent to all control modules. The first tagged
word responds by producing a read control
signal on a horizontal line. This signal
causes all bits in the selected data word to be
transmitted along vertical lines to the M
register. After the first record has been read
out, an additional control signal turns off the
tag associated with that word. Then, the process
is repeated, reading the second tagged word,
and so forth. After the last tagged record has
been read, the memory responds with an "end of
memory" signal which terminates readout.

Ordinarily the reading process is nondestructive. However, a destructive readout
is also possible. It amounts to no more than

writing zeroes into a selected word after its
original contents have been read. If a "busy
indicator" is used, a zero in it indicates that
the word is un-occupied. On the other hand, the
"busy indicator" may be eliminated and the "all
zeroes" record used to identify an empty word.
Superconductor Preliminaries
Before proceeding to a detailed discussion of the circuits, it will be convenient
to review the basic superconductor phenomena on
which the circuits are based. certain metals
such as lead and tin exhibit superconductivity,
i.e. as their temperature is reduced to a certain
critical value a few degrees above absolute zero,
they abruptly lose all electrical resistance.
The resistance can be restored by the application
of a magnetic field whose required strength is a
function of temperature. This is illustrated
by the phase state diagram. of Figure 2 which
shows the relationship between temperature and
critical field for a typical superconductor.
The region below the curve corresponds to the
superconductive state and the region above the
curve to the normal state.
If the metal is maintained at a temperature,
such as Ta, lower than the critical temperature,
Tc, then it can be switched between the normal
and superconductive states by changing the
magnetic field between Ira and Rb. This can be
done by changing the level of current in the
superconductor itself or by changing the current
in an adjacent lead as is done in the cryotron.
These phenomena provide the basis for a variety
of superconductive switching networks.
Figure 3 is an example of such a network,
called a gated persistor. The lines represent
thin film superconductive leads. The rectangles
represent thin film gate elements which can be
switched from the superconductive to the normal
state by the application of a magnetic field.
Crossing each gate and separated from it by a
thin insulating film is a control element. This
control is very narrow compared to the gate so
that current through the control produces higher
field intensities than an equal current through
the gate. Whenever a current pulse of appropriate amplitude is applied to the control, the
gate is switched. The control remains superconductive because it is made of a material
with a higher critical field.
The gated persistor is capable of storing
one bit of information in the form of a circulating current as follows: To write into the
persistor, current is applied to line W. At
point p, the current divides between paths 1
and 2, which comprise the persistor, inversely
as the inductances of these paths. Thus,

DIGITAL STORAGE AND CIRCUITS

CONTROL

DATA
__________
A ___________

r
I WORn
_._-

C\I

m en

c:
I-

I-

'I~,

iii

~OATA

WORD i

I
I

! I !

BLOCK

WORD 2
WORD I

t 1 t t t t t t t--, t t 1 1
M REGISTER

Block Diagram of an Associative Memory
Figure 1

PATH 2

PATH I

o
To

Phase :::;Ca-ce ..Jiagra.m for a I'ypical Supe.t'condl.l.cto:c

Figure 2

T
~

Gated

Persisto~

Figure 3

A SUPERCONDUCTIVE ASSOCIATIVE MEMORY

Next, a current is applied to line V making
gate 1 resistive. The IR voltage across gate 1
exponentially transf'ers 11 current to path 2.
After most of' the current has been transf'erred
to path 2, leaving 11 + 12 in path 2 and 0
current in path 1, the current in V is turned
of'f' • The distribution of' currents in paths 1
and 2 then remains constant since there are no
voltages in the loop. Finally, the Vi current
is turned OI I • Tnis causes the currents in
paths 1 and 2 to be reduced by 11 and 12
respectively. The f'inal current values are:
Path 1:

0 - 11

-II

Path 2:

II + 12 - 12

+ 11

Thus, a persisting current of 11 (clockwise)
has been established in the persistor. This
will remain until gate 1 is made resistive
again.
The process described results in a stored
one. A stored zero is represented by the absence of' persisting current. The process f'or
writing a zero is identical to that for writing
a one, except that no current is applied to line
If. The current on line V then erases any
previously stored current in the persistor by
making gate 1 resistive.
To read f'rom the persistor, current is
applied to line o. If the persistor contains
a one, then the persisting current will cause
gate 2 to become resistive and a voltage can be
detected on line O. If the persistor contains
zero, gate 2 remains superconductive and no
voltage will be detected. Note that the readout is non-destructive.

Memory structure in Detail
The Memory Bit Cell
Consider next the typical memory bit cell
i - j as shown in Figure 4. Vertical lines OJ,
~lj and Ej connect the j-th bit of' the 1-1 register
with the j-th bit of' every memory word. Horizontal lines Vi, Ci and Ri connect the i-th
control module with all bit cells of' the i-th
memory word. The bit cell consists of a gated
persistor made up of Vi, Hj, paths 1 and 2 and
gate 1, a comparison circuit comprised of' Ci,
Ej and gates 2 and 3 and a readout circuit consisting of OJ, Ri and gates 4 and 5.
To write information into this cell, a
word select signal is impressed on the Vi line
by the i-th control module and a current signal
corresponding to a one or zero is impressed
upon vlj by the j-th bit of the M register.
These two signals, properly sequenced, store

the transmitted bit exactly as in the simpler
circuit just described.
To compare a key in the M register with
corresponding keys in the memory 'fOrdS, the M
register key is transmitted along the ~v j lines
just as in writing: current f'or a one, no
current f'or a zero. At the same time, enabling
currents are transmitted on all Ej lines
corl~spondir~ to key bit positions.
La D~~ ce~
i - j, the current in \vj divides between paths
1 and 2 just as in writing. The stored and
transmitted currents combine in path 1 of' the
persistor as sun:nnarized in Table 1, vThere It
represents the transmitted current in path
1 and Is the stored current in path 1. It can
be shown that regardless of' the inductances of'
the two branches, It = Is' provided the same
vi j current is used in both writing and comparing. ~ is the resultant current in path 1.
Interpreting It = I as a transmitted 1 and Is =
- I as a stored one, Table 1. be.£.omes the truth
table f'or exclusive OR: T S + T S = T ~ S.
Thus, whenever the stored and transmitted bits
match, there is no net current and gate 2 remains superconductive. When they mismatch, a
net current exists and gate 2 becomes resistive.
Note that only if' the j-th bit is chosen as a
key is there current on Ej and is gate 3 resistive. In all columns where Ej = 0, gate 2
is shunted by a superconductive gate 3. Since
Ci contains a serial sequence of' gate pairs 2
and 3, one in each bit cell, Ci will remain
entirely superconductive if' and only if' a match
occurs in every enabled bit cell of' the i-th
word. otherwise, Ci will be resistive in at
least one column. The superconductive status
of' Ci in cells with matching keys is the tag
used to identify those cells selected by the
comparison process. In the description of' the
control module it will become clear how this
information is used in writing, reading and
clearing.
After a set of' records have been tagged
by a comparison operation, they may be read
out sequentially. Reading is accomplished by
pulsing Ri, making all gates 4 in the i-th word
resistive. Gates 5 will be resistive wherever
a one is stored. If' a current is applied to OJ,
then a DC voltage will be observed on OJ just
in case a one is stored in the j-th bit cell
of' the selected word. This voltage can be detected by a read amplif'ier associated with the
M register. After the f'irst selected record
has been read, the corresponding Ci line is
turned of'f' and the next record is read.
The Control Module
Consider next a mechanization of the
control module which will interpret Ci signals

DIGITAL STORAGE AND CIRCUITS

-1

PATH I

0
0

CURRENT STATES

TRUTH TABLE

Truth Table for Comparison Circuit
Table 1

&-.--+_-PATH I

I
Cl

Ri
I

Ri
o

Typical Memory Bit Cell i - j

One stage of the F (Ci) Network

Figure 4

Figure 5

A SUPERCONDUCTIVE ASSOCIATIVE MEMORY

from. the data modules and produce Vi and Ri
signals appropriately.

the "busy" column if a busy bit is used or by
keying with all zeroes in case that pattern is
used to designate an empty word.

The F (Ci) Network

One of the crucial operations to be performed by the control modules is the selection
of one out of many signals. For instance, in
writing, it is necessary to write into the first
empty word. In reading it is necessary to read
the first selected word. This operation is
performed by the F (Ci) network, one stage of
which is illustrated in Figure 5. 'l'ne vercJ.cal
lines continue through all control modules and
the gating shown is repeated in each. The
function of the F (Ci) network is to turn on
only that Ri which corresponds to the first Ci
which is on. This it does as follows: First
Pb is pulsed to reset all Ri' s. Then, F is
pulsed. The current travels along F until it
reaches point a in the first word counting
fram. the M register. If Cl is off, gate 2 will
be resistive and gate 1 superconductive, so the
current will pass through gate 1 and. continue
until it comes to the first word with Ci = 1.
At this point, gate 1 will be resistive and.
gate 2 superconductive so that the current will
be diverted through gate 2 to F". Once there, it
never returns to F, since in each stage either
gate 1 or gate 2 is resistive. As the current
passes from. a to b, gate 3 is made resistive
and the I current is switched from Ri to Ri.
Thus, Ri has been turned on in the first word
with Ci = 1.
Comparison
Figure 6 shows a control module connected
to one typical bit cell of the data module.
The module controls the comparison process as
follows: First, Pa is turned on making all
gates 5 resistive. At this time Pc and all Ej's
are off so that the Cils are superconductive.
Hence, the DC current I is switched into the Ci
branches. At the same time, the key is transmitted along the Wj lines so that all gates 11
reach a steady state that refle cts the state of
agreement between the transmitted and stored
bits. Now, the Ej lines are turned on in all
key bit positions, and. Pa is turned off. Wherever
a match occurs in all key bit positions of a
word, Ci remains superconductive, and. the current
remains in Ci, but, wherever a mismatch occurs
in a key bit position, both of gates 11 and 12
become resistive and the current is switched
out of Ci to Ci. Thus, in the final state, Ci
is on in just those words with matching keys.
Writing
To write into the memory, all empty words
are first tagged by comparing for non-busy words.
This is accomplished by keying with a zero on

Now, with the Ci' s on in just the empty
words, Pb, F and Pv are turned on in that
sequence. Since ~te 6 is resistive, Pv
current takes the Vi path from point v to point
Vi in all words except the first empty one.
There, gate 2 is also resisti~ because the F
current is diverted fram. F to F in that word,
Jio the Pv current divides between the Vi and
Vi paths. Next, YO J.S turned orT and gate 2
transfers all the Pv current to Vi in the first
empty word. Current in that Vi causes information transmitted along the \i j lines to be
written into the i-th word in the manner described previously. Part of the information
that is written is a "busy" indication so that
the word will not be written into again. The
writing process is terminated by turning off F
and Pv and then the Wj , s • Pb should be pulsed
to prevent circulating currents in the Vi, Vi
loops.
Reading
To read a set of records fram. the memory,
the set is first tagged by comparing all records
with an appropriate key. Ordinarily this key
will contain a one in the busy bit so that only
occupied words can respond. After a set of Ci' s
have been turned on, Pb is pulsed to turn off
all Ri's. Then the F (Ci) network is used to
turn on Ri in the first selected word by making
gate 4 resistive. Current in Ri causes readout
of the data in the i-th word as described
previously •
After the first word has been read, Pc
is pulsed. This makes all gates 8 resistive
and turns off Ci in the first selected word
since that is the only word where Ri is on,
and hence where gate 9 is resistive. Now, the
F (Ci) network can be used again to select the
second tagged record for readout. The process
is repeated until all selected words have been
read and. all Ci' s have been turned off. Then,
the next time F is turned on, the current will
remain in F to the top of the network where it
will turn on a gate which indicates that there
are no more words to be read.
It should be observed that in writing,
the F (Ci) network turns on Ri in unison with
Vi and that Pb turns off Ri and Vi in unison.
Therefore, Pc can be used to sequentially write
into a set of selected words just as it is used
to sequentially read from a set of selected
words. After each record is written, Pc is
pulsed. Gates 8 and 9 are then resistive in
the selected word and its Ci is turned off.
Then, the next record is written into the next
word.

DIGITAL STORAGE AND CIRCUITS

Po Pb

Pc
vi

Ci
2

Vi
Vi
Ci

Ri
I

I I

F Pc Pb

Control Module and Typical Bit Cell of Memory
Figure 6

Lc
~

""'"'"'

....F

F
~

F (Ci) Equivalent Network

A SUPERCONDUCTIVE ASSOCIATIVE MEMORY

The reading process, as described, is nondestructive. However, a destructive read-out
can be accomplished by following the normal
read-out by a write cycle in which zeroes are
written into the selected word, or at least
into its IIbusyn indicator.
Operating Speeds
The speed of cross film cryotron circuits
is intimately associated with the gain 01' the
cryotron. 2 Ordinarily, the cryotron controls
must be kept significantly narrower than the
gates and the interconnecting leads in order to
achieve desired gain. In a practical geometry,
the leads may be 10 times as ,vide as the controls.
Furthermore, the separation between the control
and the ground plane may be 3 times that between the leads and the ground plane. This
results in a ratio of inductances per unit
length of 30. In many circuits this implies
that the interconnecting leads contribute about
as much inductance as the controls. In such
cases, the L/R time constant of a network is
given by:

G G
l 2

2 n m f(t)

L
G
2

2(N + 1) f(t)

where Gl = the gain of cryotrons 1 and 3, G2 =
the gain of cryotrons 2 and 4, N = number of
cells in the memory, and f(t) is a function of
gate thickness only. This reduces to:

R =

4(N + 1) nanoseconds

Here, we can assume that gates 1, 2, 3 and 4
have fractional gain. Taking Gl = G2 = .4,
N = 499, we have:

300 nanoseconds

It is clear that as the number of words in the
memory increases, the speed of the F (Ci) network becomes an important factor. For very
large memories, it would be desirable to reduce
this limitation. Lower gain cryotrons could
be considered for the F (Ci) network or the
memory could be divided into functional blocks.

1
G
l

where m is the number of parallel cryotrons
which switch current from one branch of a loop
to another and n is the number of series controls
in the loop. Gl = the gain of cryotrons whose
gates are in the loop, G2 = the gain of cryotrons
whose controls are in the loop, and f (t) is a
function of gate thickness only. oFor a tin
gate thickness the order of 4000 A, this reduces approximately to:

even faster since it contains only 2 controls.
However, the F (Ci) network would undoubtedly
be slower since it contains a number of resistive .paths in parallel (the gates 3). In
order to ol2.t1m1ze the speed of the F (Ci) network,
the F and F lines which contain no controls may
be made very wide. In this case, their inductance may be ignored, and the F (Ci) network
may be represented by the network shown in
Figure 7. The L/R time constant for a worst
case condition in the F (Ci) network ( switching
from the first word in memory to the last) is
given by:

R =

4 n m nanoseconds

The relationship between gain and time constant
allows us to trade gain for speed. This is, of
course, true only i f use can be made of devices
outside the cryostat (e.g., semiconductors in
the H register) to maintain an overall gain
larger than one.
Let us consider the Ri loop of Figure 6
as an example. For a memory with 49 bits per
cell, n = 50, since each bit contains a gate 10
wi th a control in Vi. m = 1 so that the
optimum time constant defined above becomes
4 • 50 Gl G2 nanoseconds. Gates 4 and 7 may
have less than unity gain by applying larger
F and Pb pulses to compensate or by using inline cryotrons. On the basis that gates 13 are
also fractional gain cryotrons, we can assume
that Gl = G2 = .4. This gives a time constant
of 32 nanoseconds for the loop.
A similar time constant could be achieved
for the Vi loop. The Ci loop could be made

Auxiliary Circuits and Equipment
In the reading process, a voltage is
developed on line OJ. However, this voltage is
too small (,.., 300lJ. v) to be read directly. It
is therefore essential to raise the signal
level before attempting to take it out of the
cryogenic circuit. One way to accomplish this
is to have the OJ line control a high gain
cross film cryotron in an output flip-flop.
The current levels in the flip-flop would be
much larger than in the OJ line and the resistance of the output gate of the flip-flop
could also be larger than normal. Hence, the
output voltage would be large enough to detect
by external circuitry" A flip-flop of this
kind would have a relatively large reversal
time but this would not add appreciably to the
time constant for data retrieval which depends
upon the operation of other loops which include
many gates.

The e~rnal circuitry of the M register
includes flip-flops, line drivers and read
amplifiers, all of which can be mechanized

DIGITAL STORAGE AND CIRCUITS

Acknowledgements

using standard transistor techniques.
Applications
Y'any applications suggest themselves in
such areas as:
1.

Military intelligence analysis

Inventory file maintenance, and

Artificial intelligence

Most of these applications require rather large
capacities. However, there is at least one
class of problems for which a relatively small
associati".-e memory should. be "Y"eI"',f useful. These
are problems in which a large file of data must
be searched for records which match any of a
set of keys. In this case, the keys are stored
in an a.ssociative memo~r and the records of the
main file are stored in same large capacity,
serial memory such as tape. AS each record is
read from the tape, it is compared simultaneously
with all keys in the associative memory. The
trick employed here is to reverse the usual
operating procedure by storing the keys in the
associative memory and channeling the large
mass of data through the M register.
A specific application for this technique
occurs in the air traffic control problem. Here,
the main file of flight plans would be read from
a tape store and compared simultaneously with a
set of new flight plans in the associative
memory to determine whether a conflict exists.
Since a number of conflicts are searched for at
once, it is permissible that the search be
serial and hence slow.

This paper is based upon work in which
the author partiCipated as a consultant at the
Physical Research Division of Space Technology
Laboratories, Inc. The author thanks Dr. John
L. Rogers and Dr. Arthur J. learn for their
help and criticiShl.
References
1.

Seeber, Jr., R. R., ItCryogenic Associative
lvm.ory", National Conference of the A. C.
Milwaukee, 23 August 1960

M.,
2.

Cohen, M. L. and Miles, J. L., "Characteristics of Film Cryotrons", SOlid state
Electronics, Volume 1 No.4, September 1960.

Slad.e~ A. E. and McMahon,. H. 0 •• "A Cryotron
Catalog Memory System", Proceedings of the
E. J. C. C., December 1956

Kayes, M. K., "Cryotron storage, Arithmetic
and Logical Circuits," SOlid state
Electronics, Volume 1 No.4, September 1960

Goldberg, J. and Green, M. W., "Large Files
for Infor.mation Retrieval Based on
Simultaneo~ Interrogation of All Items,"
Symposium on large Capacity Memory Techniques
for Computing Systems, May 1961 (to be
published by ONR)

A CRYOGENIC DATA ADDRESSED ~IEMORY
V. L. Newhouse
R. E. Fruin
General Electric
Research Laboratory
Schenectady, New York

Abstract
A computer storage system which is addressed
by content rather than location is described. The
design has been verified by constructing and
successfully operating a three-word module consisti~g of 81 crossed-film cryotrons on a 6-inch
by 3-inch substrate.
Introduction
A typical, word organized, random access
memory system, as used in existing digital computers, is shown in Fig. 1. Each storage bit
position of such a memory uses a magnetic core
threaded by two or more selection and sense lines.
To enter an item of information into such a memory,
a location has to be assigned and selected, using
the address register and selection matrix shown in
the figure. Rence this type of memory may be
characterized as "location addressed." All conventional core memories fall into this category.
For certain problems, it is desirable to
address the memory by content rather than location.
The Data Addressed Memory (DAM), shown in Fig. 2,
has this capability. Every filled location can be
addressed by any or all of its contents. Because
all addressing functions are performed in this
manner, neither an address register nor a selection matrix is required.
For applications where the contents of the
entire memory must be compared with a specific
item of input information, a DAM has a considerable
speed advantage o¥er a conventional location
addressed system.
Such applications occur in
problems involving pattern recognition, inventory
control, document retrieval, etc. In all such
problems the DAM can compare the contents of all
its locations simultaneously with the input information, whereas the conventional memory must search
through all or part of its locations in sequence.
The large number of components with nondestructive read-out facilities required for each
location of a DAM renders the use of thin film
cryotrons advantageous. Such a system has been
suggested by P.R. Boucheron. 3 Similar systems
6
have been proposed Dy Seeber4 , LearnS, and Davies
under the name associative memory. Experimental
data addressed cryotron memories which can only
deal with a single matching location for any category have been described by Slade and coworkers. 7 ,8
*Except in certain search problems dealing with
only a few categories where "list" programming
can be used. 2

General Electric Heavy Military
Electronic Dept.
Syracuse, New York

A small model of a magnetic data addressed memory
using a modification of the domain wall viscOSity
effect for non-destructive read-out is described
by Kiseda, et al.10,11
System Description
The Data Addressed Memory which is the subject
of this paper is shown schematically in Fig. 2 and
in detail in Fig. 4. It used shielded Crossed
Film Cryotrons l for switching and storage. The
cryotrons are interconnected by lead films which
stay superconducting at all times during operation.
Storage is performed by setting up circulating
currents in various storage cells as described in
greater detail below. Since any current distribution established in a completely superconducting
network is stable, positive feedback circuits
analogous to Eccles-Jordan flip-flops need not be
used in superconductive systems.
The functions of a DAM will be described in
terms of a specific problem, that of cataloging
books in a library. For instance, each memory
word location might contain the title, author's
name, subject and shelf location of a particular
book. Each category of information would be
restricted to a specific portion of the word. If
the book is to be listed under several subjects,
it would be entered in several locations. In each
location, the title, author's name and shelf location would be duplicated.
To gain access to information on a specific
book, its title is entered into the appropriate
positions of the input-output register of Fig. 2.
The system is then switched into its comparison
mode. In this mode the title position of the inputoutput register is simultaneously compared with the
corresponding position of every storage location.
vlherever a "matching" location is found, i.e.,
wherever the title stored in the location matches
that in the input-output register, a current is
switched into the upper branch of the so-called
comparison line connected with that specific location (see Fig. 4).
In many cases of practical importance the
contents of several locations will match, so that
several links of the comparison line wi 11 have been
"set". To deal with this problem sequencing circuits are included in the control lo~ic of Fi8. 2
which inhibit access to all matching locations
except that one nearest to the input-output
register.
Once the presence of a matching location has
been established, the system can be switched to its

DIGITAL STORAGE AND CIRCUITS

read-out mode in which the contents of the whole
of the matching location are duplicated in the
input-output register. Alternatively, the system
can be switched to its write mode. In this case,
new information is written on top of the information in the selected location. A word is erased
by rewriting it as all zeros. The control logic
ensures that access to the selected location is
not lost even if the information in it is changed.
When the nearest matching location has been
dealt with, and before looking for the next
nearest one, persistent current is induced in the
so-called comparison bypass cell attached to the
first selected location. This allows the location
to be "bypassed" during subsequent matching
cycles. vlithout changing the contents of the inputoutput register, the system is now put through
another comparison cycle. The sequencing logic
allows access to the second nearest matching location. ~fuen this location has been dealt with,
its bypass cell is activated thus allowing access
to the third nearest matching location. When no
further matching location exists a signal is
produced by the control logic. The comparison and
bypass cells of all the previously selected locations can now be reset simultaneously, thus releasing the system for interrogation with a nevI title.
If new information is to be entered into the
memory the system is first interrogated with a
title consisting solely of zeros. Access is thus
automatically provided to the first empty location
if one exists.
System Operation
The Storage and Comparison Cell
The principle of the circulating current
storage cellI used throughout the memory is illustrated by the digit loop in Fig. 3. The right and
left legs of the loop are of equal inductance. A
stored "I" is defined as a clockwise circulating
current of 1/2. To establish this, a current of
magnitude I is applied to the digit line in a
downward direction. Simultaneously, a write line
current is applied driving the write cryotron
resistive and forcing the digit current to the
right leg. The write current is then removed,
followed by the digit current. Since the legs are
of equal inductance, this leaves a current of 1/2
circulating in the clockwise direction in the loop.
A "Oil is defined as a counterclockwise circulating
current of 1/2. It can be established in a similar
manner using a digit current of magnitude I in the
upwards direction.
Comparison of Stored and Applied Information.
If a current correspondin;~ to a "I" (I downwards)
is appiied to a cell in which a !!l" is stored
(l/2 cw) or a "0" is appliec1 to a cell in which a
"0" is stored, the applied and stored currents will
add in the ri6ht leg and cancel in the left leg.
A "I" applied and a 110" stored or a "0" applied
and a Ill" stored will add in the left leg and
cancel in the right leg, Thus a match between
applied and stored information is indicated by a

current of magnitude I in the right leg and a mismatch by a current I in the left leg. Figure 3
shows how a match or mismatch is sensed by the
match cryotron in the top branch of the comparison
line. If a number of these bits are assembled into
a word and a comparison is made on all of the bits
in the word the top comparison branch will be
superconducting only for an exact match.
Comparison on a Portion of the Word. It is
usually desirable to match with only a few of the
bits that make up the word, ignoring the other bits.
This can be achieved by providing a comparison bypass branch around the match cryotron at each bit
position. This bypass branch is disabled in any
bits used in the comparison by applying "comparison
bit selector" currents. Thus the comparison line
will be superconducting only if all interrogated
bits in a word match the corresponding bits of the
app lied word.
Readout of Stored Information. Figure 3, also
shows a readout capability incorporated in the
cell. In this configuration the comparison branches
in each bit position of the selected word are also
used for readout. This requires, if more than one
match exists, the switching of current from the
top comparison branches of all non-selected words
as described below.
To read out stored information a "0" digit
current of magnitude I is applied upwards. This
current divides, sending 1/2 upward into each leg.
These currents combine with the stored circulating
current of 1/2. If a "0" has been stored the
result will be a current I upwards in the right
leg and no current in the left leg. If a "I" has
been stored the result will be a current I upwards
in the left leg and no current in the right leg.
Thus a stored "0" will switch the mismatch cryotron
resistive, forcing the comparison current through
the comparison branch in that bit, leaving the
sense cryotron superconducting. A stored "1" will
switch the match cryotron resistive, forcing the
comparison current through the comparison bypass
branch, switching the sense cryotron resistive.
Consequently, when a current is applied to the sense
line a voltage will De read there for a "1" but not
for a "0".
Selection and Control Logic
The function of the selection and control
logic is to locate the first matching location that
falls into the category i)eing searched, so that
read and write operations can be performed on that
word only, and finally after that word has been
processed, to have it bypassed during Subsequent
comparisons. These operations are performed by the
sequencing ladder, the access inhibitor cells and
the comparison bypass cells shown in Fig. 4.
The Sequencing Ladder. The sequencing ladder.
shown separately in Fig. 5, selects the word of the
class being searched that is stored nearest the
"top" of the memory. The ladder is controlled by
the comparison branches from each memory location.
In the case of a "matching" word, current flows in

A CRYOGENIC DATA ADDRESSED MEMORY

the top branch; in a mismatched location it flows
in the bottom branch. In all words before the
first match, the control rungs will be blocked by
a current in the bottom comparison branch. For
instance, Fig. 5 shows cryotron Bl driven resistive
for a mismatch in word 1. Cryotron Al remains
superconducting, allowing current to flow from the
top of the ladder down to word #2. Here, where
the first match occurs, the rung will be superconducting (cryotron B2) and the left rail resistive. The current will deflect from the left rail
to the right rail through the superconducting rung,
identifying this word as the first matching word.
Since this current is now in the right rail, it
cannot reach matching words further down the ladder.
A match is indicated externally if no voltage
appears across the rails of the ladder. If no
match exists, all the rungs will be resistive and
a voltage will ue sensed across the ladder.
Access Inhibit Cells. These cells are shown
in Fig. 4. Their function is to inhibit access to
all words except the selected one, by storing a
circulating current. This current is first stored
in all of these loops simultaneously by applying
sequential and overlapping current pulses to the
access inhibit set line and the access inhibit line.
In the selected word, this circulating current
will be quenched due to current in the control rung
of the ladder. This allows write and comparison
bypass set currents to operate on the selected word.
It also enaDles comparisons other than the selected
one to be overridden. By applying a read-out
strobe pulse, comparison currents in all unselected
words will be diverted to the lower comparison
branch. Only in the first selected word will the
comparison current remain in the top comparison
branch. It is this operation which enables the
comparison line to be used for read-out.

This comparison can be made on the basis of ~
or all bits that are contained in the word. Any
bits-that are not pertinent can be masked out of
the comparison.

On those bits that are to be compared, a
digit current corresponding to a "I" or "0" and
a comparison bit select current are applied. On
those bits that are to be masked from the comparison, only the digit current corresponding to a "0"
is applied.
Next, the comparison set iine is puised. In
those words where a match exists, the comparison
current (which is always kept on) is forced to the
top comparison branch. This switches the sequencing ladder current (which is maintained throughout
the comparison cycle) through the rung of the first
matching word. It is blocked from the rungs of all
non-matching words.
Overlapping and sequential access inhibit and
access inhibit set pulses are next applied, storing
a current in all access inhibit cells. This current will be quenched in the first matching word
by the current in the rung of the sequencing
ladder.
Access to all but the first matching word is
inhibited by the currents now stored in the access
inhibit cells. Therefore Read, Write and Comparison Bypass operations will be effective-oDly on
the first matching word.
It is of interest to note that sequential
access to all the locations in the memory irrespective of their content can be obtained by comparing
with all the input-output register bits masked.
This procedure is required when the memory is to be
filled with zero's before commencing operations.

The Comparison Bypass Cells. These are used
2. Read - The Read Operation must always be
to eliminate a matching word from further considera- preceded by a CompariSOn operation.
tion after operations on it have been completed.
The top branch of the Comparison line is used
This is accomplished by storing a circulating
current in the associated comparison bypass cell
for reading. In all matching words the comparison
current has been diverted to this branch of the
thus making cryotron L in the top comparison branch
comparison line. By pulsing the read-out strobe
resistive. A current is stored in the cell by
the comparison current will be switched to the
applying overlapping and sequential pulses to the
lower comparison branch in all except the first
comparison bypass set lines and the comparison bymatching word. This happens because the first
pass lines. The access inhibit cells ensure that
matching word is the only one that does not have
the comparison bypass set current is routed to the
current stored in its access inhibit cell. Thus
comparison bypass cell in the selected word only.
the comparison current can be maintained through
Once ~ circulating current has been stored in this
cryotron I, only in the first matching word.
cell, blocking a match for the previously selected
word, the system can be returned to the comparison
All masked bits have "0" digit and sense curmode to search for the next matching word. After
rents applied. A stored "I" in the selected locaall matching words have been processed the comtion will then be indicated by a voltage on the
parison bypass reset current is applied, quenching
sense line of that bit. The unmasked bits need not
circulating currents in all comparison bypass
be read out since they are already known.
cells simultaneously.
Modes of Operation
These are discussed in connection with Fig. 4.
1. Comparison - The contents of all words in
the entire memory can be compared simultaneously.

3. Write - The Write Operation must also be
preceded by a Comparison Operation. (To write in
the first empty register a match is made with all
O's).
Digit currents are applied (corresponding to
the word to be written) followed by a write pulse.

DIGITAL STORAGE AND CIRCUITS

Digit currents are required even for masked bits.
Therefore it will be necessary to read out the
masked bits and re-write them.
4. Comparison Bypass - This operation is used
to exclude the first matching word from further
consideration after it has been dealt with. A current is stored in the comparison bypass cell of
the first matching word by applying overlapping
and sequential comparison bypass and comparison
bypass set currents. When all matching words have
been bypassed, an attempt to match will result in
a voltage across the sequencing ladder. The comparison bypass currents are then erased by applying a comparison bypass reset.
Experimental Results
Several Data Addressed Memory plates have
been tested in all modes of operation. An arbitrary pattern was stored and various comparisons
were made. Read) Write and Comparison Bypass
operations were also performed. These tests were
performed by manually switching DC currents of 200
mao
Time constant measurements were made on
several loops using single 200 rna. pulses. These
measurements were in agreement with the time constants calculated from the geometry. The method
used l was to store a current in a loop. This current was quenched by switching a cryotron in the
loop (identified as the 'switch' cryotron in
table I), resistive for an interval less than the
calculated time constant. The current remaining
in the loop was monitored by measuring the critical
gate current of a 'sense' cryotron controlled by
this current. This method was used to measure the
following:
1. The time constant for transfer of a current from the lower to the upper branch of the
comparison loop when pulsing the Comparison Set.
2. The time constant for transfer of a current from the upper to the lower branch of the
comparison loop when pulsing the read-out strobe
in the presence of a persistent current in the
access inhibit cell. This differs from the previous time constant because there is a low inductance
resistive path in parallel with cryotron I.
3. The time constant for quenching a circulating current in the Access Inhibit cell.
4. The time required to invalidate a match
in words I and 2 and to transfer the sequencing
ladder current from word I to word 3. This was
measured by observing the quenching of a circulating current in the Access Inhibit loop of word 3.
Typical results of these measurements are
shown in table I. (The switch and sense cryotron
identifications refer to Fig. 4.) Nominal CFC
dimensions are shown in table II. The widths and
lengths of the various interconnections are indicated in Fig. 6 which is a photograph of the
actual layout.

Discussion
Future Prospects
Since in the present work the substrate area
was larger than any published previously, and since
the logic design had never been previously tested,
the crossed film cryotrons used were deliberately
made large, and an extremely low density layout
was used. By reducing the cryotron dimensions
(operating at a somewhat lower temperature to maintain gain), and by using a denser layout, it should
be possible to accomodate sixteen 2l-bit words on
the presently used substrates. 1000 such substrates
interconnected and contained in a 1 cubic foot
cryostat, would constitute a memory of useful capacity. Approximately 160 input-output leads would
be required for such a system.
Since substrate-to-substrate interconnections
possess a WJch higher inductance than those printed
on the substrates, it is desirable to design the
system so that interconnections are not included in
loops driven by cryotrons. Several of the ladder
circuits such as the comparison bypass set circuit
do not satisfy this criterion but can be modified
so that they do. A simple ladder circuit is shown
schematically in Fig. 7A. The interconnection
inductance will limit the operating speed of such
a circuit. This problem can be overcome by the
modification shown in Fig. 7B, at the cost of an
extra bypass line on each plate. By using this
bypass line, current can be directed through any or
none of the other lines on each plate. Since the
interconnection inductance is not included in a
cryotron loop, it no longer affects the circuit
operating speed. This technique is also useful for
minimizing the effect of sneak currents, and has
been discussed previously in this connection. 9 It
should be mentioned that in this type of circuit
the comparison bypass set current will initially
divide equally between all lines on one substrate.
Thus, there must be enough lines on one plate to
limit this current to a safe value or the current
rise time must be limited to prevent partial
switching in un!;elected words.

A more complex type of circuit, in which the
top rung of the ladder on one plate controls the
bottom rung of that on the next plate, is required
for the sequencing ladder because this serves as
the data transmission channel between plates. The
time delay in this circuit can probably be reduced
to the vicinity of 50 nanoseconds by using a
special low inductance interconnection between the
plates together with some extra cryotron amplifiers.
This time delay will probably be the factor limiting overall system speed since in the comparison
cycle a signal may have to be propagated through
every substrate.
Conclusions
The experiment described above proves that
fully operating crossed film cryotron circuits can
be obtained on 6-inch by 3-inch substrates. In
assessing this result it should be taken into
account that because of the specific purposes of

CRYOGE~IC

DATA ADDRESSED MEMORY

this project, no component redundancy was used and
all film deposition was performed under the simplest
manual control. The good circuit performance under
these rigorous conditions is probably due to the
use of ample design tolerances and to the operation
of the storage cells such that no controls ever
have to distinguish between different non-zero current amplitudes.
For example, a worst case analysis of the cell
of Fig. 3 leads to a comparison ratio of 6.5/1.
This is the ratio of current in the right leg of
the storage cell to the current in the left leg of
the storage cell in a "matching" bit and includes
consideration of a five percent change in inductance of one leg due to layout and fabrication
variations, a 10 percent change in digit current
due to driver drift, and a transfer of only 90
percent of the digit current from the left leg to
the right due to incomplete switching. This allows
a large margin for variation in control widths,
cryotron parameters or drift in operating point.
Another advantage inherent in the properties of the
DAM is that if access to a faulty location can be
inhibited, system operation will not be affected,
(except that the number of available locations is
reduced by one).
Estimates presented in the preceding section
indicate the feasibility of a 300,000 bit memory
with a 50 microsecond comparison cycle time. Such
a system should be particularly valuable since i t
is quite compatible with existing room temperature
data processors.
Acknowledgments
The authors would like to extend sincere
thanks to P.R. Boucheron for his major contributions to the data addressed memory mentioned in
the text; to J.W. Bremer with whom some of the
earliest superconducting devices incorporated in
the memory were evolved; to D.A. Donath for
valuable criticism; and to R.E. Tanis who fabricated the cryotron circuits.
References
1.

V•L. Newhouse, J. t.J. Bremer, and R. R. Edwards,
"The Crossed Film Cryotron and Its Application
to Digital Computers," Proc. E.J.C.C., pp.255260; December 1959.

N.S. prywes ana 11 • ..1. Gray, Jr., !!nulti-List
Organized Associative Memory," Moore School of
Electrical Engineering, University of Pennsylvania, January 1962.

P.R. Boucheron, General Electric Co.-RMED,
Syracuse, N.Y., private communication.

R.R. Seeber, Jr., "Associative Self-Sortin;;
Memory," Proc. E.J.C.C., pp. 179-188;
Decemoer, 1960.

A.J. Learn, "Superconducting Computers,"
Electronics,vo1.3~pp.50-5l; November 24, 1961.

P.M. Davies, "A Simplified Superconductive
Associative Memory," Proc. S.J.C.C.; May, 1962.

A.E. Slade and R.O. McMahon, "A Cryotron
Catalog Memory System," Proc. E.J.C.C., pp. 115120; December 1956.

A.E. Slade and C.R. Smallman, "Thin Film Cryotron Catalog Memory," Solid State Electronics,
vol. 1, pp. 357-362; September, 1960.

V.L. Newhouse, "Superconducting Circuits for
Computing Machines (Review),;; ElectroTechnology, vol. 67, pp. 78-89; April, 1961.

10. W.L. McDermid and R.E. Petersen, "A Magnetic
Associative Memory System," IBM J. Res. and
Dev., vol. 5, pp. 59-62; January, 1961.
11. J.R. Kiseda, R.E. Petersen, W.C. Seelbach
and M. Teig, "A Magnetic Associative Memory,"
IBM J. Res. and Dev., vol. 5, pp.l06-l2l;
April, 1961.

DIGITAL STORAGE AND CIRCUITS

INPUT - OUTPUT REGISTER

WORD #2

H
SELECTION
MATRIX

MEMORY CELLS
LOCATION ADDRESSED MEMORY SYSTEM.

FIGURE 1

SEQUENCING
LADDER

~WORD

I I

ACCESS
INHIBIT
CELLS

COMPARISON
BYPASS
CELLS

INPUT - OUTPUT REGISTER

BIT #1

BIT #2

BIT #3

COMPARISON
LINE

~ ~ ~
I

I
I

~ ~ ~

CONTROL AND SELECT ION LOGIC
FIGURE 2

I:~:~:
I

I'~'~'

MEMORY AND COMPARISON CELLS

DATA ADDRESSED MEMORY SYSTEM.

WORD n

A CRYOGENIC DATA ADDRESSED MEMORY

COMPARISON
BIT SELECTOR

DIGIT

WRITE
SENSE
CRYOTRON
MATCH
CRYOTRON
WOIT~

" I \. I ' -

MISMATCH
CRYOTRON

TOP
COMPARISONl....4-+---+-----L---L...J
BRANCH

COMPARISON
BYPASS
BRANCH

SENSE
CRYOTRON
FIGURE 3

ACCESS
INHIBIT CELLS

COMPARISON
BYPASS CELLS

MEMORY CELL.

BIT I

BIT 2

BIT 3

~(r-_ _.A.A_ _----"

ACCESS ACCESS READ-OUT COMPARISON
COMP.
COMP.
COMPARISON
INHIBIT INHIBIT STROBEr;BYPASS SET~
BIT
BIT
BIT
SET ~
I
./WRITE
SENSE DIGIT SEL. SENSE DIGIT SEL. SENSE DIGIT SELECTOR

n II

COMPARISON
SET

~'"

H~DG-I-4-+-JI~4-~~~~~~~-+-~-+~-+--+i~t
KI

COMPA RI SON >--+1~A-f1+-+-+-E..-,If-.-+-+t::tJH~1~-t:j
t:j
~

trl
r:J)

WRtTF~
~~'-+I--+-I_
COM~FUSON

r-ii~~'~

__ ,

COM~lI<\SO""

.'T SIH.,£cTb12:,

~
o

L.INE

~"I" ~d1::lJ

co1JlPAti:!\'$O,""
.'T S1U...£CTOFt.

II~~

C;O==t~~

SEQutcMC\NG
L. A "'DEft

COfl'\PAR~'SO~

CO"" PAR'S01'4
9V ...A55

PASS

.'T SELe.c.rolit

~ES&.:r

II
o

I I I

I I ! I

I I I

! I

I I I

I I ! I

II
3

I ! I

I I I

.I'

, !

i
6

'NCHES
FIGURE 6

DATA ADDRESSED MEMORY LAYOUT.

DIGITAL STORAGE AND CIRCUITS

FIGURE 7A

SIMPLE LADDER.

FIGURE 7B

MODIFIED LADDER.

A CRYOGENIC DATA ADDRESSED MEMORY

SUBSTRATE :IF

TEMPERATURE IN OK
OPERATING
T
~T
Tc

NOMINAL
TIME CONST.
CFC GATE SWITCH SENSE IN MICROSEC.
RESISTANCE CFC
CFC MEAS. CALC.

12/5/61

3.714

3.635

0.079

280

12/6/61

3.710

3.630

0.090

300

1/3/62

3.831

3.752

0.079

700

1/12/62

3.807

3.741

0.066

700

1/10/62

3.707

3.621

0.086

250

5.0

5.4

2.0

1.8

1.0

1.5

LI ,L2

5.0

TEST RESULTS.

TABLE I

WIDTH

THICKNESS

MICRONS

Pb SHIELD

1.0

SiO INSULATION

0.8

1600

0.3

0.8

1.0

330

1.0

LAYER

Sn GATES
SiO INSULATION

_. r ACTIVE
!-ID

I 3

CONTROLS

1INACTIVE CONTROLS I
TABLE II

CONSTRUCTION

DETAILS.

REMARKS
MANUAL SWITCHING OF
COMPARISON FUNCTION
ALL MEMORY FUNCTIONS
DEMONSTRATED
H3 HELD RESISTIVE
COMPARISON LOOP
TIME CONSTANTS
ALL MEMORY FUNCTIONS
DEMONSTRATED
ACCESS INHIBIT
TIME CONSTANT
REACTION TIME OF
COMPARISON LOOP AND
SEQUENCING LADDER

101

CIRCUITS FOR THE FX-l COMPUTER
Kenneth H. Konkle
Staff Member, Digital Computer Group, Lincoln Laboratoryllo
Massachusetts Institute of Technology
Lexington, Massachusetts
Summary

to those having relatively high load impedance.

A set of computer logic circuits capable of
50-megapulse operation is described. Included are
("f'O+O~
~1'i~ TYI;V;1'1c.r
0"""'" ..... _ ....................................a....L. ........... oI."-O

1""\,11co
1:" ....... -'-..... -

omnl-i-P;o,.....c
..... _ ,

.......... u.1:"-'-..I. ........... -

.......

c+o+-i,....

"" '-''-"\1 ........ _

-Pl;T\_
..t:""

.................

flop, a diode logic unit with current-steering
amplifier, a passive delay line, and an active
variable delay circuit, all of which are designed
to operate with terminated 75-ohm transmission
lines. Ten-nanosecond pulses and 20-nanosecond
flip-flop transition times are achieved through
use of very-high-speed MADT transistors. The
circuits have been successfully employed in the
FX-l, a small general purpose computer with a
high-speed magnetic-film memory.
I.

Introduction

The FX-l Computer is a small, high-speed,
general-purpose digital computer designed and
built, at the Massachusetts Institute of Technology, Lincoln Laboratory, to be a realistic
test vehicle for high-speed logic Circuits,
1
packaging techni~ues, and magnetic-film memory.

In addition to the L-5447, a few 2N781
germanium epitaxial mesa and 2N708 silicon
epitaxial mesa transistors were used where their
higher current and dissipation capabilities were
needed.
Design Constraints
At the desired speeds the transmission delay
associated with just a few inches of wiring
becomes comparable to the rise time of the signals.
Terminated transmission lines are, therefore,
indicated for most of the logic circuit interconnections in order to reduce crosstalk and
reflections.
Since transmission line impedances are
relatively low, the logic circuit is a transformer-coupled pulse amplifier so that the high
load impedance needed for best ~e3formance from
the transistor can be provided. '
II.

It is a parallel, binary, stored-program
machine with a 12-bit word length (plus parity)
and addressing capability for 1024 words.
The
present memory, however, contains 256 words plus
a 16-word toggle switch storage for read-in and
check-out programs. The transistor logic circuits
operate at a 50-megapulse rate; that is, the
contents of flip-flop registers may be interchanged or modified at 20-nanosecond intervals.
The magnetic-film memory has a read-write cycle
time of 350 nanoseconds. Approximately onemillion single-address instructions can be performed per second. The instruction code is fairly
small but provides relative and deferred addressing. The total number of transistors in the
machine exclusive of memory is 3500.
Transistors
The logic circuits have been designed around
a germanium p-n-p Microalloy Drift transistor, the
L-5447, which was deVelOPed and brought into production early in 1960 by the Lansdale Division of
Philco Corporation with support from Lincoln
Laboratory. A later smaller version of this
transistor is the T-22l7, and commercial modifications are available as the 2N769 and 2N976.
The important characteristics of this tranSistor,
as shown in Table I, are its high gain-bandwidth
product and its low base resistance, collector
capacitance, hole-storage, and saturation voltage.
However, the gain-bandwidth product falls off
above 10 mao of collector current as shown in
Fig. 1, thus limiting the class of usable circuits
*Operated with support from the U.S. Army, Navy,
and Air Force.

Circuits

Gated Pulse Amplifier
The gated pulse amplifier, shown in Fig. 2,
is somewhat unusual in that it has degeneration in
the emitter circuit. Its operation can be demonstrated by considering the effect of a negative
1.7-volt step applied to the input (the base of
Ql), assuming that the gating point (the collector
of Q2) is grounded. The input voltage and the
emitter resistor determine a maximum value for
the collector current in Ql. This current is more
than ade~uate to bring the transistor into
saturation, thereby applying the supply voltage to
the divider consisting of the collector RC network,
the pulse transformer and its load, and the
emi tter RC network. However, the current. in the
magnetizing inductance of the transformer
increases with time until eventually the available
collector current is exceeded. The transistor
then comes out of saturation and terminates the
output pulse.
This circuit combines the advantages of
saturated operation (the output is determined
primarily by passive components) with the fast
turn-off time of a nonsaturated circuit. If an
output pulse from a similar circuit is applied to
this circuit, the pulse is amplified and restandardized to a minus 1.7-volt peak amplitude and a
10-nanosecond width. Shorter than standard pulses
are lengthened by hole storage while longer pulses
are shortened by the shaping action described
above.
The capacitor in the emitter circuit speedsup the output rise time. The most important

DIGITAL STORAGE AND CIRCUITS

102

function of the RC network in the collector is to
reduce the collector supply voltage at the end of
the pulse so that the peak collector voltage is
reduced during the transformer overshoot. The
collector RC network also causes some droop in
the output pulse, although this has not been found
objectionable. The overshoot voltage of the output pulse is determined by the magnetizing inductance of the transformer and the load resistance,
which is always 37 ohms, hence no clamping is
re~uired to limit the back voltage on the trfu~
sistar.
The design of the pulse transformer is
crucial to the correct performance of this
circuit. It is wound on a very small pair of
Ferramic Q2 cup cores. The 14-turn primary and
3-turn bifilar secondary are wound over each other
with the distributed capacitance and inductance
carefully controlled in order to provide the
proper characteristic impedance and resonant
fre~uency.
The secondary turns are lumped near
the end of the primary which is ac grounded.
A special cable terminator is used at the
input to the pulse amplifier to compensate for
the capacitive, non-linear input impedance. A
100-ohm resistor can be used with some increase in
rise time and delay.
Transistor Q2 of the gated pulse amplifier,
Fig. 2, enables or disables the amplifier. If Q2
is saturated the circuit operates as previously
describedj however, if the gate transistor is cut
off, collector current will not flow in Ql and an
output pulse w~ll not be produced. Stray capacitance at the gating point is charged to minus
1.1 volts when Q2 is cut off, in order to prevent
a spurious output pulse. Since the pulse
amplifier draws current from the gate transistor
only when it is amplifying a pulse, Q2 may be used
to enable or disable several amplifiers, provided
the amplifiers are not pulsed simultaneously.
Several gate transistors may be paralleled to
obtain more complex gating logic. The gate
transistor input, which is either at 0 or minus
1.8 volts, comes from a flip-flop or other level
amplifier via a terminated 75-ohm transmission
line. Up to 5 gate transistor inputs can be
driven from a 75-ohm line.
Each pulse amplifier can drive two 75-ohm
linesj if only one line is used, a 75-ohm padding
resistor must be added. The output of a line may
drive two pulse amplifiers if they are located
within several inches of each other. Thus a fanout of four is obtained with certain geometrical
limi tations •
The output pulse from the gated pulse amplifier has a minus 1.T-volt peak amplitude, JO-nanosecond width, 2-nanosecond rise time, 3.5-nanosecond fall time., and 1.3-volt overshoot. The
circuit exhibits unity voltage gain for input
pulses larger than minus 1.3 volts and has
essentially no output for input pulses srn.aller
than minus 0.5 volts. This provides good
discrimination against spurious pulses and noise,

and

ade~uate

margins with normal pulses.

The pulse propagation delay in this circuit
is 3 nanoseconds of which nearly half occurs in
the transformer. A change in the gate transistor
input level must precede the input pulse by at
least 10 nanoseconds to produce a proper output
pulse. This "gate set-up time" is a function of
stray capaCitance at the transistor collector.
The maximum repetition rate for the pulse
amplifier is limited to 25 megapulses per second
by transformer recovery time. However, this
limitation only rarely prevents the FX-l from
operating at. an effective rate of 50-million
register transfers per second.
~~xing

Pulse Amplifier

A further extension of the basic pulse amplifier is shown in Fig. 3. In this circuit, the
mixing pulse amplifier, transistor Q3 is added
between the collector of the pulse input transistor and the pulse transformer in order to isolate
the input transistor (now called a pulse inverter)
from the large voltage swing at the transformer
primary. Transistor Q3 operates as a grounded-base
amplifier with a small amount of base degeneration.
It saturates during the pulse and unsaturates at
the end in a manner similar to that of the original pulse amplifier. The input signal to the
mixing transistor is approximately 1.5 volts with
a pulse current of 15 ma.j hence, the input impedance is 100 ohms. Several parallel pulse inverters
may feed this low-impedance point, producing an
output pulse whenever an input pulse is applied
to anyone of them. As is shown in Fig. 3, pulse
inverters may be gated by gate transistors as in
the case of the gated pulse amplifier. Because
of the third transistor, the pulse delay time is
increased to 4.5 nanosecondsj however in all other
respects its characteristics are e~uivalent to
those of the gated pulse amplifier.
Fig. 4 shows an input and output pulse for a
mixing pulse amplifier. The slight ringing is due
to the distributed capacitance of the transformer
windings.
Flip-flop
The circuit schematic of the flip-flop is
shown in Fig. 5. Transistors Ql and Q4 are mixing
pulse amplifiers similar to those previously discussed. The pulse transformers have been modified
to provide secondary center taps. Transistors Q6
and Q7 form a conventional saturated RC-coupled
flip-flop. Triggering is accomplished by driving
both the "offl! and "on" transistors to their new
states by the input pulse. As a result the output transitions} as seen in Fig. 6, are very symmetrical. In addition, this triggering method
improves the rise and fall times of the output
since the capacitors in the cross-coupling aTlns ai'
the flip-flop can be made smaller. These
capacitors need only remove the stored charge
from the lN903 silicon mesa trigger diodes.
Transistors Q5 and Q8 (2N781's) are output

103

CIRCUITS FOR THE FX-l COMPUTER

emitter-followers, each capable of driving a
single terminated 75-ohm line. Resistors placed
in series with the bases of the emitter-followers
prevent oscillation and ringing on the outputs.
Standard output levels are 0 and minus 1.8 volts
with rise and fall times of 5 to 8 nanoseconds.
Note that the clamp voltages for the flip-flop
are locally generated by the silicon diode net in
the upper right corner. This has been done in all
FX-l packages in order to simplify power distribution. Transistors Q2 and Q3 provide steering
for the complement input. These transistors are
similar to mixing pulse amplifiers; however, their
bases are biased from the outputs of the flipflop. Therefore, an inverted pulse applied to
their common emitters is steered either to the
clearing or setting transformer. As seen in
Fig. 6, the delays within the flip~flop, due to
the transformers, diodes, etc~, are greater than
10 nanoseconds, which is adequate to allow pulse
dodging. The flip-flop can be used in shift
registers or for register interchanges without
auxillary delay or storage. Each input terminal
can be driven from up to 6 pulse inverters, with
an input pulse arriving at one terminal or another
at 20-nanosecond intervals. The pulse inverters
may be conditioned by gate transistors as
described in the pulse amplifier discussion.
The transition times of the flip-flop are less
than 20 nanoseconds.
Register Driver
The circuits previously described comprise
the bulk of those in FX-l. Several others are
required for the control and in-out sections of
the machine. One of these is the register driver
which is used to amplify connnand pulses for
driving a flip-flop register. It consis~s of a
mixing pulse amplifier followed by a groundedbase amplifier using an NPN silicon epitaxial mesa
transistor and an output transformer. It will
Qrive eight 75-ohm lines with an output pulse
slightly wider and slower than that obtained from
a standard pulse amplifier.
Timing Circuits
The control section of a computer requires
circuits which can generate the chains of connnand
pulses needed to perform instructions. In most
computers, these command pulses are obtained from
a clock, however, in FX-l they are obtained from
a large complex multipath delay-line loop. The
exact path taken through the control is a function
of the states of control flip-flops. Hence, a
sequence of pulses in spa~e and time is produced
which is determined by the instruction to be
performed. This type of control was used because
it is more easily realized in a machine employing
pulse logic circuits.
Delay Line
Two types of delay are used in generating
the pulse sequences. One is a passive delay line,
the other an active variable delay circuit. The
passive delay line, shown in Fig. 7, is a folded

strip-transmission line etched on one side of
thin double-clad etched-wiring stock. By using
a very thin dielectric, O.Ol-inch thick Teflon,
and narrow lines, a delay of 4 nanoseconds at
75-ohm impedance can be obtained in an area of
approximately 2 square inches. Due to the
fineness of the strip line there is a signal loss
of 0.035 volts per nanosecond. Therefore, a
special pulse amplifier was designed which
produces a 60% larger pulse for driving the
delay line. This pulse can traverse up to
40 nanoseconds of passive delay line before it
is attenuated to the point that it needs amplification. Approximately 300 of these lines are
used for spacing and trimming high-speed connnand
pulses.
Variable-Delay Circuit
The active variable-delay circuit, shown in
Fig. 8, is used for delays exceeding 45 nanoseconds, as for example, in memory-strobe timing,
parity-check timing, and carry-propagation timing
in the adder. Transistors Ql and Q2 form a
single-shot multi-vibrator which is triggered by
turning on Q2. The lower lN903 diode at the
collector of Q2 applies a positive step to the
82-~~f. timing capacitor. When the capacitor has
charged, Ql starts to conduct again, cutting off
Q2. This same diode then opens allowing the
pulse transformer to overshoot. This overshoot
is amplified and standardized by the output pulse
amplifier to produce the delayed pulse. Delays
can be produced in the range from 45 to 160 nanoseconds; larger values require adding an external
capacitor.
Diode Logic Circuit
When a large number of terms are to be combined into a single gating function, pulse logic
is not desirable because the pulse must be passed
sequentially through a pulse amplifier for each
term involved, resulting in an excessively long
logic delay. Level logic reduces the delay by
producing the complex gating function for a
single pulse amplifier. It is also superior for
memory parity computation, where it permits the
use of a pyramidal rather than a serial arrangement of gates.
The parity function of 4 bits can be obtained
with a 3-level logic circuit, that is, an "and/or/
and," if the inputs are available in both their
normal and inverted forms. Normal and inverted
gating functions are also necessary in delayline-loop control logic, since a pulse is usually
routed down either one or another of several
delay paths. These requirements were met by
using a 2-level diode-logic net followed by a
current-steering amplifier which provides the
third level of logic and the complementary output
levels. The outputs of the current-steering
amplifier are shifted with Zener diodes, clamped
to locally generated voltages, and then amplified
by emitter-followers so that terminated output
lines can be driven. Several additional inputs
were added to the diode net so that the unit

DIGITAL STORAGE AND CIRCUITS

104

would be more generally useful.
Fast silicon mesa diodes (lN903's) are used
in the diode nets, L-5447 transistors in the
current-steering amplifier, and 2N781 epitaxial
mesa transistors as the emitter-followers. The
delay time of this level logic circuit is 10 nanoseconds; the input and output levels are at 0 or
minus 1.8 volts.
Level Amplifier
The level amplifier is an RC-coupled
saturated L-5447 inverter driving a 2N781 emitterfollower, similar to half of the flip-flop of
Fig. 5. It has a delay of 6 nanoseconds, and
1~rill

dri"tie one

75=o~bm

line with standard FX-l

levels having 5- to 8-nanosecond rise and fall
times.
S cILll1i cLt Tri gge r

coaxial cable, RG-187U. The second method uses a
three-layer etched-wiring board with the center
layer as a ground plane; the width of the etched
lines on the faces, and the insulation thickness
between them and the ground plane are controlled
to produce 75-ohm strip transmission lines.
Connections to or through th~ ~round plane are
made with plated-thru-holes. '
Figure 12 shows a cross-section of the threelayer etChed-wiring board. It is constructed by
first etching two tray cards; one has the vertical
wiring, the other has the horizontal wiring and
the ground plane. Clearance apertures are etched
in the ground plane where, connections are not
desired to the plated-thru-holes. The two cards
plus two veY)T thin cover layers are then l~llinated
together and drilled. When the holes are drilled,
the copper edges of the wiring lands and ground
plane are exposed. Copper is then chemically
deposi ted and. folloT:led

The Schmidt trigger circuit, Fig. 9, is used
to amplify and sharpen slowly changing signals
coming from Switches, push buttons, or the lower
speed logic circuits of the in-out equipment. Its
output is a standard FX-l level which can, if
desired, be applied to a special pulse amplifier
to produce a standard FX-l pulse on the negative
transition of the input signal.
III.

Construction

A three-level method of construction is used
in FX-l. Circuit components are wired into small
plug-in-units which plug onto trays. These trays
contain most of the logic interconnections and
are in turn plugged into boxes which contain the
intertray wiring. This 3-level arrangement
reduces the size of the machine and the wiring
delays, without limiting accessibility.
Plug-In-Units
The circuit components are assembled in a
cordwood fashion between two double-sided etchedwiring cards with plated-thru holes to form the
plug-in unit, Fig. 10. Each unit, which measures
1 3/4" x 2 1/4" X 1", contains approximately 60
components and 10 transistors, which corresponds
to one flip-flop or four gated pulse amplifiers.
Small commercially available components are used,
including 1% molded deposited carbon resistors
and miniature ceramic capacitors. The assembly
of the cordwood units proved to be Quite simple
and, contrary to expectations, repair has also
been easy. Approximately 360 plug-in-units of 13
different types were used in FX-l.

The tray, shown in Fig. 11, will mount and
interconnect up to 20 plug-in-l.l..11i ts • The entire
high speed central processor section of the FX-l
was built on 26 of these trays, 12 of which are
identical. Figure 11 shows the two interconnection methods used on FX-l trays. The first
method uses 75-o~~ Teflon-insulated miniature

b~l

heavy electroplating.

This copper on the two cover-layer faces is
finally etched away leaving plated-thru-holes
wi th small lands around them.
FX-l was initially run using trays with
coaxial-cable wiring. Eight of these have since
been replaced by their etched-board equivalents
with excellent results, and the remainder will be
replaced in the near future.
Complete Machine
Figure 13 is &..11 overall view of the FX-l in
its temporary frame. The central processor is
located in the upper left in three boxes, each
containing up to 10 trays. The trays plug into
86-pin double-sided printed circuit connectors,
from the rear of the computer. Transmission line
wiring of the tray is carried through the connectors as a wire pair with one side grounded.
Intertray connections on the front of the boxes
uses RG-187U coaxial cable.
Cooling is obtained with low velocity air
f'r()m t.hp. 'bRock ()f' t.hp. c()mrmtp.r,

The 256 word magnetic film memory with its
drive circuits and sense amplifiers is located
in the bottom left. The racks to the right
contain the power supplies, control panel, toggle
switch storage, in-out buffer and control, photoelectric tape reader, and XY-display scope.
IV.

Results & Conclusions

The circuits described in this paper have
been used to build a computer, the FX-l, which
can perform instructions in less than one microsecond, and whose acc-wnu.laLor <.;an add two 12-bit
numbers in 160 nanoseconds. The 3500 transistor
central nrocessor has been in ODe ration since
July 196i. Debugging of the ma~hine proceeded
very rapidly. All signal waveforms were extremely
clean and free from noise. Since initial
debugging, the operation of the central processor has been reliabl@ and entirely satisfactory.

CIRCUITS FOR THE FX-1 COMPUTER

105

Although the operating speeds were referred
to as 50 megapulse per secondj that is, 20 nanoseconds per register transfer, these speeds have
not yet been obtained. At present, a 24-nanosecond register transfer rate is used because of
the long gate-set up delayj however, modifications
to the gate transistor circuit are now being
studied which will allow operation at the stated
speed.

Maximum Ratings
Collector Voltage, V
CB
Collector Voltage, V
CES
Collector Voltage, V
CEO
Emitter Voltage, V
EB
Total Device Dissipation at 25°C

The circuits and construction tec~~iques
employed are adequate for the construction of
larger high-speed computers with improvement
needed only in the flexibility of the level logic
circuit and the component packing density.
V.

-12 volts
-7 volts
-2 volts
35 row

Electrical Characteristics
Static Characteristics

min

Collector Cutoff Current,
ICBO (VCB = -5v)
Emitter Cutoff Current,
lEBO (VEB = -2v)

Acknowledgement

The author wishes to thank Leopold Neumann
and John Laynor who were deeply involved in the
circuit design, Elis Guditz who was largely
responsible for the construction techniques
employed, and to Dr. Donald Eckl whose group
supported the transistor development contract.
VI.

-12 volts

IX:! Current Gain,

typ

max

0.3

.05

-20 rna, VCE = -0.5v)
Saturation Voltage, VC~(SAT)
(IC = -10 rna, IB = -0. rna)

.16 .25 v

Base Input Voltage, V~
(IC = -10 rna, IB = -0. rna)
High

1. Raffel, J. I., T. S. Crowther,
A. H. Anderson, and T. O. Herndon, "Magnetic Film
Memory Design," Proceedings of the IRE, vol. 49,
no. 1, pp. 155 - 164, January 1961.
2. Carroll, W. N. and R. A. Coopper, "Ten
Megapulse Transistorized Pulse Circuits for Computer Applications," Semiconductor Products J
vol. 1, no. 4, pp. 26 - 30, July/Aug. 1958.

1 rna

(IC

References

!-La

Fre~uency

340

Characteristics

Output Capacity, Cob
(VCB = -5v, ~ = 0, f

4 mc)

Input Capacity, C'
b
(VEB = -lv, IC = 0, f

4 mc)

G~in Band~dth~

( ifCE

= -O.)V,

430 mv

= 20

1.5

3 pf

4.5

8 pf

100

250

600

850

2S nsec

rna

f = 80 mc)
3. Neumann, L., "Transistorized Generator
for Pulse Circuit Design," Electronics, vol. 32,
no. 4, pp. 47 - 49, April 3, 1959.

Gain Bandwidth, f'7
(VCE = -5v, ~ = rna,
f - 200 mc)

4. Gudi tz, E. A., "Plated Component Connections for Micro-miniature CirCuits," Proceedings
of 1959 Electronic Components Conference,
Philadelphia, Pa., pp. 166 - 171.

Hole Storage Factor, K'
s
(I B = 2 rna)

5. Guditz, E. A., "Connections Plated with
Wiring," Electronics, vol. 32, no. 51, pp. 96 - 97,
Dec. 18, 1959.

2000~1

Table I
Important Characteristics of L-5447 & T-22l7

IIII

1000~--r---~----~~

6. In the field of education,
some of the far-reaching possibilities
inherent in a meld of "programmed instruction" and digital computers have
become evident to many.

"'+-C!

UV...l..\,..; ..... V....f,.. ......

'h,,+-

t.J\..II.V,

o;:>+-

'--'Vv

+-'ho
v ...

.&.\,..;

",0;:>,.,.,0

..." ........

.&, ''-'.

+-;,.,.,0
V-'-J'~'-'"

,-'10

'-"1- ...... - -

...... \A...Ii' ..............

no;:>T'\O;:>'h;';+-~o",
,,""""'tJ
. . . . . . ., ............. v ...... "-u

0;:>,..,,-'1

u.. ...... '"""

+-'ho

v ..... '-"

T'\,..,o,-'1I"\""';"'O;:>+-O'""T
,t-'.&-

\,..o\".ll.V4"

................... V\"..o...l..J

tailed control by computers. Several
groups are currently interested in
"semi-automatic laboratories."

computer capabilities to create an
integrated system for goal-oriented,
on-line-inventive information'processing.

The foregoing considerations
suggest that man-computer communication
will be an active field during the next
few years and that efforts to facilitate
productive interaction between men and
computers will receive wide appreciation.

In aSSOCiating capabilities a
through f primarily with human beings
and capabilities g through j primarily
with computers, we are of course describing the present state of affairs,
the technology in which we now must
work, and not asserting any essential
discontinuity between the domains of
human and machine information procesSing. There is always the possibility
that human competence in g through j
can be significantly increased, and it
is almost certain that machine
competence in a through f will develop
rapidly during the next decades. At
present, however, we think that man and
computer complement each other, and that

~~n-Computer

Complementation

The fundamental aim in designing a
man-computer symbiosis is to exploit
the complem ntation that exists between
human capab lities and present computer
capabilitie
a.
human;

To select goals and criteria --

ON-LINE MAN-COMPUTER COMMUNICATION

the intellectual power of an effective
man-computer symbiosis will far exceed
that of either component alone.
steps Toward Man-Computer Symbiosis
To bring men and computers together
in tight synergic interaction, we must
make advances in several contributory
fields. Among the most important appear
to be: time sharing and other possible
solutions to the economic problem;
memory and processor organization for
contingent retrieval of information and
programming of procedures; programming
and control languages; and on-line
input-out equipment, including integrated
displays and controls. The groups with
which we are associated have been working
in those areas. It is disappointing to
fin~ that the areas appear to grow more
rapidly than we can explore them and to
realize how trivial are our accomplishments relative to the requirements.
However., we are beginning to have some
tangible results, and it may be worthwhile to illustrate briefly the following three:
1. A system for computer-aided
teaching and computer-facilitated study.
2. A man-computer system for use
in the planning and design phases of
architectural and constructional problems.

3. Two programs that display aspects of the internal processes of a
computer during execution of programs.
Computer-Aided Teaching and Learning
Exploration of ways in which a
computer can facilitate teaching and
learning raises several problems in mancomputer communication. Effective
teacher-student relations involve nearly
continuous interchange of information,
and anything that interferes with the
communication is likely to impair
effectiveness.
The importance of rapid, convenient
student-teacher communica.tion ha.s
demonstrated itself quite clearly in
experiments with a simple, automated,
language-vocabulary-teaching system.
One version of the system, Tutor 1, uses
a computer typewriter as the communication link between the student and the
machine. Let us examine first the
procedure briefly and then the problem
of typewriter communication between
student and computer.
The typescript of the sample GermanEnglish lesson, shown in Fig. 1,

115

illustrates the procedure. In a session
with Tutor 1, the student initiates
activity by typing "0. 11 The computer
then asks him whether or not the student
wants detailed instructions. The
student replies by typing "Sll for "No,
start the lesson.1I The computer selects
a German word at random and presents it.
The student then types an English word
that he thinks is equivalent in meaning
and terminates his reEponse by hitting
the IIcentered-dot '! key. If the response
is acceptable to the computer, the compu ter types II +11 for II c orrec t. II (Brevi ty
is crucial.) If it wants another
English equivalent, the computer then
types the German word again. If it does
not want another English equivalent, it
types the item score and the cumulative
score to date and offers a comment on
the student's performance. When the
student misses a word, the computer
types "-" for "incorrect" and "ta" for
"Do you want to try again?" If the
student replies "y" for "yes, II the computer presents the missed German word
again. If the student replies "n" for
"no," the computer types an English
equivalent and requires the student to
copy it. And so forth, as illustrated.
The first thing we found out about
Tutor 1 was that students (children and
adults) who type well like to use it,
whereas students who do not type well
may be attracted at first but soon tire
of the lesson. During the development
of the program, several variations were
tried out. Those that speeded the pace
of presentation or streamlined the
procedure of response were the most
successful. A version that eliminated
the requirement that the student type
the response -- that allowed him to
respond vocally or subvocally and then
trusted him to score his answer -- was
greatly preferred by students who typed
only fairly well or poorly; good typists
liked IItype-the-answer" versions better.
With one type-the-answer program, designed to avoid all possible interruptions, students who type well sat for
two or three hours at a time, industriously adding new German, French, or
Latin words to their vocabularies,
occasionally checking their cumulative
scores, but never asking for coffee
breaks.
Twenty years from now, some form
of keyboard operation will doubtless be
taught in kindergarten, and forty years
from now keyboards may be as universal
as pencils, but at present good typists
are few. Some other symbolic input
channel than the typewriter is greatly
needed.

MAN-MACHINE COOPERATION

116

We make some use of the light pen
and "light buttons ll associated with
mul tiple-choice questions and anSvJers
displayed on the oscilloscope. When the
alternative courses of action can be
laid out in a tree-like branching
structure, it is convenient to let the
computer ask a multiple-choice question
via the oscilloscope display and to
arrange the program in such a way that
touching the light pen to the button
associated with particular response
brings forth a subordinate question
appropriate to that response. With
four familiar alternatives, the operator
can make a selection every second or
two (i.e., select at a rate of 1 or 2
bits per second), which is adequate for
some purposes, though not truly
competitive with talking or expert
typing (up to 20 and 40, respectivelYJ
bits per second in situations in which
the pace is not limited by judgmental
processes) .
In computer-aided teaching, the
restriction to a small ensemble of
multiple-choice responses sometimes
precludes truly convenient, natural
communication, and it leads into
controversy with those who think that
the "constructed response" methods are
inherently superior. In our work thus
far, it appears that the difference in
effectiveness between constructedresponse and multiple-choice procedures
is small compared with the difference
between a convenient, fast response
mode and an inconvenient, slow one.
Convenience and speed influence markedly
the student's enjoyment of his interaction with the computer and the lesson.
The most important sub-.goal, we believe,
is to maximize the amount of enjoyment,
satisfaction, and reinforcement the
student derives from the interaction.
And good student-teacher communication
appears to be absolutely essential to
that maximization.
Good man-computer communication is
important, also, in systems in which
the computer serves to facilitate
learning without taking the initiative
characteristic of most human teachers.
We are working on a system, Graph
Equation, the aim of which i"S'""t()
facilitate a student's exploration of
the relations between the symbolic and
graphical forms of mathematical
equations.
The program displays, for example,
the graph of a parabola (see Fig. 2),
and below the graph it displays the
equation,

y=a(x-b)

(1)

Associated with each of the parameters,
a, b, and c, is a potentiometer that
controls tne value of the parameter.
The student can vary the parameter
values at will and see, directly and
immediately, the correspondence betvleen
the configuration of those values and
the shape of the parabola. We are in
the process of substituting, for the
potentiometers, "light scales" with
pointers operated by the light pen and
of displaying numerical coefficients
instead of letter parameters on the
oscilloscope. Even in the present crude
form, however, the system is an
effective aid. It presents the linkage
between the symbolic and the graphical
representation in a dynamic way, It
lets the student explore many more
configurations than he could explore if
he had to plot graphs on paper. And
it lets him see "answers" while he is
still thinking about "questions" -something we think may be very important
in learning.
We plan, of course, to have the
Graph Equation system operate
dynamically in the other direction,
also. The student will draw a rough
parabola. The computer will fit an
accurate parabola to the rough one and
display the accurate one. At the same
time, the computer will calculate and
display the coefficients. The
completed system, we hope, will provide
the student with a flexible, responsive
study tool. It will not have much
practical value as long as it is restricted to parabolas, of course, but
it should be pOSSible, with a faster
machi~e~ .to ~a~dle ~ourie~ ~:an~~?rm~,
convolut10n 1ntegra~s, ana tne ~lKe.
Often the student must manipulate
characters of text with reference to
pictorial or graphical information. He
have been able to handle some of these
functions but still lack an integrated
system for communication of interrelated
symbolic and pictorial information between the student and the computer.

* The work on computer-aided teaching
and learning is supported by the United
states Air Force under Contract No.
AF33(616)-S152 and is monitored by the
Training Psychology Branch, Behavioral
Sciences Division, Aerospace Medical
Research Laboratory, Aeronautical
Systems Division, Air Force Systems
Command.

ON-LINE MAN-COMPUTER COMMUNICATION

Computer-Aided Planning and Design
In starting to explore the field of
computer-aided planning and design of
systems, we have focused on hospitals.
Hospitals pose very interesting and
difficult -- and we believe to a large
extent typical -- system problems because the relative importance of the
various planning factors. varies from one
local context to another, because so
many kinds of interest and experience
are relevant and eager to make themselves felt, and because tangibles and
intangibles are so intimately interrelated. One of the main aims in setting
up a computer system to facilitate
hospital planning is therefore to
provide a means through which general
guide lines and local constraints can
interact. Another is to permit several
persons with various backgrounds and
interests to look at tentative plans
from their own differing points of view
and to manipulate and transform the plans
during the course of their discussion.
A third (since the intangible factors
must ultimately be converted into
tangible, physical form) is to give the
planners a way of sketching out their
suggestions and then relating them,
quickly and conveniently, to all the
other considerations that have been
introduced.
Coplanner, a computer-oriented planning system with which we have been
working, is essentially:
1. The PDP-l computer with typewriter, oscilloscope, light gun, and
magnetic-tape unit.
2. An ensemble of empirical data
describing the commerce (communication
of information, transportation of objects, and movement of personnel) that
goes on in typical hospitals.

3. An ensemble of programs for
accepting, storing, retrieving, processing and displaying information.
In our work thus far with Coolanner.
we have experimented with hypothetical hospital situations, using two or three
members of our own group and an outside
expert or two as the planning team. In
preparation for a team planning session,
we load into core the programs most
likely to be wanted first and make ready
the tapes containing the rest of the
programs, the ensemble of empirical data,
and the material generated in previous
planning sessions.

117

The members of the planning team
then sit before the oscilloscope. They
start to discuss, for example, a hospital
that is expanding its plant and must
relocate and enlarge its X-Ray Department. They come to the question: Where
should the X-Ray Department be located,
relative to the other departments and
facilities, in order to minimize the
cost of its interdepartmental commerce?
One of the members of the team retrieves, through the computer, a record
of previous analyses that provides data
on the major components of X-Ray commerce:
a.

transport of patients,

b. trips by doctors and internes
to supervise x-ray examinations, to study
x-ray films, and to consult with
personnel of the X-Ray Department,
c. communication not involving
movement of personnel, and
d. routine personnel activities
such as entering or leaving duty stations
and taking meals and breaks.
In response to typewriter commands,
the computer then prepares and displays
several graphs to summarize the quantitative commerce data. The graphs are
mainly distribution graphs and histograms. Since they refer to hospitals of
the same type and size, but not to
precisely the one being planned, intuitive judgment suggests modifications to
take into account various features of
the local context. Members of the team
make the adjustments in the process of
discussion. All they have to do to increase the height of a bar in a histogram is to touch the top of the bar with
the light pen and lift it to the desired
level. Usually there will be discussion
of the change and several successive
adjustments of the graph. If the graph
is a frequency histogram, raising one
bar automatically lowers the others.
Efforts have been made to create a
favorable context for exercise of the
planners' intuitive judgment, Provision
is made for labeling, filing, and later
processing alternative quantitative
summaries if the planners do not agree
fully on a single summary.
Figure 3 shows two graphs of the
type developed in this phase of the
planning discussion.
The planners of course have several
different ideas concerning the new layout
of the hospital. To make these ideas

118

concrete, they display prepared floor
plans -- a separate plan for each floor
of each version -- or sketch them
directly on the screen of the oscilloscope, using the light pen as a stylus.
Sketching is facilitated by the computer,
which posts a background outline plan
having the proper dimensions and showing
existing structures that cannot readily
be altered. In its "straight-line" mode,
the computer plots straight lines even
if the sketcher's lines are wavy. In its
" preferentially-parallel-to-axes" mode,
the computer plots lines precisely
parallel to the x axis if the sketcher
makes them approximately so, etc. On
their sketches, which they can readily
file away and recall for revision, the
planners label the various departments
and the stairs, elevators, dumbwaiters,
etc. Each label; typed on the typewriter~
appears at the top of the oscilloscope
screen, and then is adjusted to desired
size, trapped by the light pen, moved to
its proper location on the plan, and
dropped there. Each label serves as a
storage and retrieval tag for the sketch
to which it is attached. The plan can
therefore be made up in small parts and
displayed as a whole. vii thin a few
months, the program will be capable of
filing and retrieving assemblies by name.
Having tentatively worked out their
ideas about X-Ray com~erce and sketched
several physical arrangements, the
planners now turn to the problem of
evaluation. First, they select one of
the commerce-distribution hypotheses and
one of the physical layouts for exami~
nation and deSignate them as input data
to a fast-time simulation program that
converts the commerce pattern from a set
of statistical distributions to a
sequence of individual trips and calls.
Then they apply a program that finds the
best routes for the trips and calls and
computes expected durations and costs.
In calculating cost, the amounts of time
spent by various categories of personnel
are weighted appropriately. The weighting
function can, of course, be discussed
and varied by the planning team. The
calculated cost provides anevaluative
measure for the selected layout under
the selected commerce hypothesis.
Actually, several different evaluative
formulas are ordinarily used. The corresponding cost figures are saved for
later use.
The evaluative procedure is then
applied to other combinations of layout
and commerce hypotheSiS. When all the
combinations have been treated, the
planners recall the cost figures and
compare them. On the basis of this

~fAN-:MACHINE

COOPERATION

comparison, they usually discard all but
the best two or three schemes. They
modify the best ones, introduce new considerations developed as a result of the
study, and make further simulation and
evaluation runs.
Figure 5 shows an output-display
prepared by the evaluation program.
If the planners are inclined to go
into detail in certain areas, Coplanner
is prepared to assist them. An elevatorsimulation routine, for example, provides
a dynamiC display of elevator operation
under the loads specified by a selected
commerce-distribution hypothesis and a
determination of best routes. Direct
dynamiC simulation has important roles
to play in work of this kind because it
appeals to non-mathematical planners
more directly than does queuing-theory
analysis performed with the aid only of
symbolic assumptions and equations.
Sometimes dynamiC simulation is a substitute for the abstract theory; sometimes it is an introduction to the
abstract theory; sometimes it is a check
upon the abstract theory.
In the preceding discussion, one
small facet of the hospital planning
problem was used to illustrate the approach we are advocating. We have
developed a fairly powerful system to
facilitate planning in the area discussed and in related areas. In other
areas, the system is only starting to
develop. The computer parts of the
system are not intended, we should
emphasize, to calculate optimal plans or
designs; they a~e intended to provide
memory, manipulative, computing, and
display functions in such a way that
they can be integrated with the more
intuitive functions supplied by the
human parts of the system.*
Visualizing the Operation of
Computer Programs
The covertness of the operation of
the programs of electronic computers
makes it difficult for us to develop of
them the same direct, perceptual kind
of comprehension that most of us have
of familiar mechanisms, the moving parts
of which we can see and touch. The
great speed with which the programs run

'*Coplanner was developed under USPHS
Project W-59, Collaborative Research in
Hospital Planning. J.J. Souter, A.I.A.,
and M.B. Brown, M.D., past and present
Project Directors, and J.I. Elkind and
W.E. Fletcher partiCipated in the
formulation of the system.

ON-LINE MAN-COMPUTER COMMUNICATION

adds to the difficulty, of course, but
we are in the habit of solving the speed
problem -- for example, through "slow
motion." Unless a window or a plastic
model will provide solution, however, we
are in the habit of letting the problem
of covertness go unsolved. We tend to
be satisfied with extremely indirect
procedures for interrogation and for
drawing inferences. In the case of the
human brain, for example, a neurophysiologist may try to construct a
model of an internal process on the oaS1S
of waveforms recorded from 10 or 100 of
the million or billion neurons involved,
plus microscopic inspection of several
slices of the tissue prepared in such a
way as to render visible one or another
feature of its architecture. Our approach to computers is comparable: When
trouble arises and the results do not
turn out as we expect them to, we may
try to figure out what is going on by
examining with the aid of a typewriter
control program the contents of supposedly critical registers, one register at
a time, even though we cannot hope to
look at more than a hundred of the
thousands or tens of thousands of
registers involved. Alternatively, we
may ask for a printout of the contents
of many registers at some particular
point in the running of the program,
hoping to reconstruct the dynamic pattern
of events from the static view provided
by the printout.
Considering the problem posed by
covertness leads one to think about the
procedure, introspection, used as the
basic experimental tool in such early
psychological laboratories as Wundt's
and Titchener's, and still widely employed in the development, if not in the
formal testing, of psychological
hypotheses. Human introspection is a
useful procedure despite its severe
shortcomings. How much more useful it
would be if those shortcomings were
overcome -- if all the processes of the
brain were accessible to the reporting
mechanism; if the reporting mechanism
could describe all the aspects of those
processes; if the reports were detailed
and accurate; if introspecting did not
interfere with the process under
examination.
That thought,leads immediately to
the idea of a computer analogy to, or
improvement upon, human introspection.
Clearly, computer introspection can be
freed of all the shortcomings mentioned,
except the last, and the last one can be
turned to advantage. Displaying its own
internal processes will of course inter-

119

fere with the computer's execution of its
substantive programs, but only by
appropriating memory space and time.
Often, there is memory space to spare,
and programs normally run too fast for
the operator to follow them perceptually.
The conclusion, therefore, is that it
might be interesting to experiment with
programs that display various aspects of
the internal operation of the running
computer.
~wo such progr~ns, written for the
PDP-l computer, are Program Graph and
Memory Course. Program Graph was written
with the hope that it woura-racilitate
the introduction to computer programming
and provide displays through which
certain individual or "personality"
characteristics of programming style may
be seen. Memory Course ~as intended
mainly for use in "debugging" computer
programs. Both programs make use of a
trace routine that executes the instructions of the object program in
normal, running sequence and, after each
execution, (a) records in core registers
the contents of the accumulator, inputoutput register, and program counter,
(b) does some incidental bookkeeping,
and (c) turns control over to the display routines. The display routines
develop graphs of types to be illustrated.

The graphs displayed by Program
Graph are illustrated in Fig. 6. In
~6A, as each instruction of the
object program is executed, its location
is plotted as ordinate, and the cumulative
number of executions is plotted as
abscissa. (Roughly speaking, therefore,
the graph represents active memory
location versus time.) Both the ordinate
and the abscissa scales run from 0 to
1777 (octal). The interpretation of the
graph is quite direct: straight-line
parts of the graph represent straightline parts of the program; jumps represent jumps or subroutine calls; serrations represent loops. The subroutine
structure is revealed clearly. If the
operator knows the general course the
program should follow, he can detect and
locate gross faults readily.
Figures 6B-6D show, for the same
object program, the contents of the
accumulator as a function of time. The
abscissa scale again runs from 0 to 1777.
In Fig. 6B, the ordinate scale covers
the range from _217 to 217; in Fig. 6c,
it runs from _213 to 213; and in Fig.
6D, it runs from -27 to 27. Evidently,
the accumulator is heavily engaged in
computations involving small numbers.

MAN-MACHINE COOPERATION

120

Figures 6E-6G show, for the inputoutput register, what Figs. 6B-6D showed
for the accumulator.
Figure 6H displays the instruction
codes. Each inst~uction code is a twodigit octal number. The ordinate scale
extends from 02 (and) to 76 (operate,
which is an augmented instruct1on, the
augmentation not shown). The most
heavily used instructions are 20 (load
accumulator with contents of) and ~
(deposit contents of accumulator into).
Figure 61 displays the memory references and the augmentations. Both are
shown here; either class may be
suppressed.
In Fig. 6J, all the graphs of Figs.
6A-6I are displayed simultaneously. Because the points are shape-coded, it is
possible, though difficult, to reconstruct in detail the sequential pattern
of a program from graphs of this type.
They might therefore find application
in historical documentation of very
critical computations, such as those
concerned with rocket launching and air
defense. In any event, the composite
representation conveys an impression of
the great capability computer's have to
introspect upon their internal processes
and report about them in detail.

Program Graph and Memory Course
are but two of many possible schemes for
displaying the internal processes of the
computer. We are working on others that
combine graphical presentation with
symbolic presentation. Syrriliolic presentation is widely used, of course, in
"debugging" routines. If many symbols
are displayed, however, it is not
possible to proceed through the program
rapidly enough to find errors in
reasonable time. By combining graphical
"Ji th symbolic presentation, and putting
the mode of combination under the
operator's control via light pen, we
hope to achieve both good speed and goo~
discrimination of detailed information.
Problems to be Solved in
Man-Computer Communication
Among the problems toward which mancomputer symbiosis is aimed -- problems
that men and computers should attack in
partnership -- are some of great intellectual depth and intrinsic difficulty.
The main problems that must be solved to
bring man-computer symbiosis into being,
however, appear not to be of that kind.
They are not easy, but their difficulty
seems due more to limitations of technology than to limitations of intelligence.
What we would like to aChieve, at
least as a sub-goal, is a mechanism that
will couple man to computer as closely
as man is now coupled to man in good
multidisciplinary scientific or engineering teams.

As we leave this topic, we should
perhaps mention the phenomenon that
appears when Program Graph is equipped
for recursive operation and set to
display its own operation. The result,
of course, is only a recursion of
beginnings, terminated by overflowing
of the pushdown list. This effect is
not entirely foreign to human introspection.
Tne routine, Memory Course, plots
a grid-like map of memory and displays,
against the background of the grid, the
course through memory taken by the object program. The dots of the grid
represent memory registers, and the dot
that represents the register containing
the instruction presently being executed
is encircled. As control passes from
one instruction to another of the object
program, a line is drawn connecting the
corresponding registers. The effect is
hard to illustrate in a still photograph
because its effectiveness depends largely
upon the kinetic character of the'displav.
However, Fig. 7 may convey an approxi:
mate impression. Because the photograph
integrates over time, it shows a longer
segment of the program's course through
memory than one sees when he views the
oscilloscope directly.
v'

For a psychologist to telephone a
mathematician and ask him, "How can I
integrate J (dx/{1-x 2 ) )?" required, in
one empirical test, 105 seconds, including 65 seconds devoted to dialing
and formalities with the mathematicianis
secretary plus 32 seconds of preamble
with the mathematician. To ask the
mathematician that particular question
is, of course, wantonly to waste his
time -- 170 seconds of it, in this case,
since all he needed to say was: "Look it
up in any table of integrals," and all
he did say was that sentence embedded in
a context of encouragement and courtesy.
(TO find a table of integrals 2 and then
to locate the entry took the psychologist,
who missed the relevant formula on his
first pass and started over at the beginning after scanning 569 entries. 7
minutes and 25 seconds.)
-

Preliminary study of these displays
of internal computer processes was
supported through a contract with the
Council on Library Resources.

ON-LINE MAN-COMPUTER COMMUNICATION

121

What we would like the computer to
do for us, in the context of the foregoing
example, does not require such a deep
solution as an algorithm for formal
differentiation; it requires merely good
communication and retrieval. We would
like to have an arrangement that would
let the psychologist write on his desk
input-output surface:

J
-

= what?

(2)

..I.-A

and then let the computer replace the
"what?"
in perhaps 2 or even 20
seconds -- by the expression:

In the example, our aspiration
would not stop, of course, with the
display of expression (3) in symbolic
form. The psychologist would surely
want elucidation. His next request
might be "Please plot a graph, Ii or, if
the novelty were worn off, simply
" Graph. " We would then like to have the
computer display on the input-output
surface a figur~such as Fig. 140 in
Dwight's Tables.
The figure would, of
course, be plotted from computed points,
not retrieved from storage. It would
be no trouble for the computer to calculate and present it in a few seconds.
(For the psychologist to plot a rough
graph of the integral took 12 minutes.
For another person to locate a
published figure (Dwight's) took 17
minutes: a little more than 16 to get to
the document room and thumb through
books that did not contain the figure,
and then a little less than 1 to pick
up Dwight's book and scan as far as
page 29, where the figure is.)
Five Immediate Problems
Consideration of many such examples
as the foregoing and of what would have
to be done to put the computer's clerical
power conveniently and responsively under
the control of human initiative suggests
that the main essential steps to mancomputer symbiosis are the following:
1. For the economic reason
mentioned in the Introduction, develop
systems for sharing the time of digital
computers among many users on a splitmillisecond basis. With J. McCarthy and
S. Boilen, one of us is working on a

small-scale prototype of such a system
with five user stations.*
2. Devise an electronic inoutoutput surface on which both the· operator
and the computer can display, and through
which they can communicate, correlated
symbolic and pictorial information. The
surface should have selective perSistence
plus selective erasability; the computer
should not have to spend a large part of
its time maintaining the displays. The
entire device should be inexpensive
enough for incorporation into a remote
console. An interesting approach to
the man-to-machine part of 4th is problem
is being taken by Teagher.
We are
employing an oscilloscope and light pen
to fulfill the function, but they do not
meet the cost and selective-persistence
requirements.

3. Develop a programming system
that will facilitate real-time contingent
selection and shaping of informationprocessing procedures. The system must
permit trial-and-error operation based
upon Iltentative computation ll : it will
often be necessary to go back to the
beginning or to an intermediate point
and to try a different attack. We are
experimenting with interpretive systems
for on-line assembly of procedures from
sub-procedures,** and we are planning
work on console compiling, intermeshed
with testing and contingent application
of procedures as they are required by
the human components of the man-computer
partnership.
4. Develop systems for storage and
retrieval of the vast quantities of
informa tion required to support, .simultaneously at several user stations,
creative thinking in various areas of
investigation. For economic reasons,
such systems must almost certainly be
hierarchical, moving information from
large-capacity, fast-access storage as
(or shortly before) the information is
needed. To achieve the desired effectiveness, it will probably be necessary to
make advances in the direction of
parallel-access, associative memory with
preliminary activation based upon apperceptive relevance. In this area, we
believe, much fundamental study of

* The work on time-sharing is supported
by Grant R68568 from the National
Institute of Health.
**One of the systems is based on a typewriter control program, Process Control,
written by D. Park.

122

information indexing and of memory
organization will be necessary before
truly satisfactory hardware can be designed, but it appears that quite a bit
can be accomplished directly through
development of memories -- probably
read-only memories -- with very large
capacity and moderately fast access and
through the application of existing
keyword or descriptor techniques.
5. Solve the problem of human cooperation in the development of large
program systems. It appears that the
development of effective human cooperation and the development of man-computer
symbiosis are "chicken-and-egg" problems.
It will take unusual human teamwork to
set up a truly workable man-computer
partnership, and it will take mancomputer partnerships to engender and
facilitate the human cooperation. For
that reason, the main tasks of the first
time-sharing computer system with many
remote stations may tolell be in the areas
of language and procedure development.
In the five problem areas just
mentioned, "to begin is everything,"
even if it is necessary at first to
build research systems along lines that
would be uneconomic for widespread application. If we neglect the arguments
of economics and elegance we can think
at once of ways of solving, or at least
starting to solve, the problems. These
ways will probably be adequate to test
the premise that man-computer symbiosis
will be able to achieve intellectual results beyond the range of men alone or
of computers programmed and operated in
conventional ways.
Four Long-Term Problems
In four other areas, the problems
to be solved appear -- if they are not
simplified beyond recognition in the
effort to make them tractable -- to be
deep and intrinsically difficult. The
first of these areas is computer
appreciation of natural written language~
in their semantic and pragmatic as well
as in their syntactic aspects. The
second is computer recognition of words
spoken in context by various and unselected talkers. The third is the
theory of algorithms, particularly their
discovery and simplification. The fourth
is heuristic programming. We believe
that these four areas will in the long
term be extremely important to mancomputer symbiosis, but that man-computer
partnerships of considerable effectiveness and value can be achieved without
them. We suspect that solutions in
these areas will be found with the aid

MA:-.J"-MACHINE COOPERATION

of early man-computer symbioses, rather
than conversely.
An Intermediate Problem
A system combining an elementary
form of computer speech recognition,
computer recognition of carefully handprinted characters, and simple light-pen
editing techniques, would provide, we
think, a very convenient and effective
communication link between man and
computer.
The problems involved in
creating such a system seem to us to be
intermediate between the five and the
four. They may be solved in time to
permit the use of correlated voice-hand
input in the earliest man-computer
partnerships, but, if the required
solutions are not ready, it would not be
good to wait for them.
References
1.

James J. Souder, Madison Brown,
Weldon Clark and Jerome Elkind,
Collaborative Research in Hospital
Planning, united states PUblic Health
Service, Project W-59, to be
published in the spring of 1962.

B. O. Peirce, A Short Table of
Integrals, 3rd edition, Boston: Ginn
and Company, 1929.

H. B. Dwight, Table of Integrals and
other Mathematical Data, 3rd edition,
New York: The Macmillan Company, 1957-

H. M. Teager, Semi-Annual Progress
Reports dated January 1961, June 1961
and January 1962, M.I.T. Computation
Center. Also, Quarterly Progress
Reports 2, 3, 4 and 5 of the RealTime Time-Sharing Project, M.I.T.
Computation Center.

ON-LINE MAN-COMPUTER COMMUNICATION

123

o
Good afternoon. This will be
your German-English Lesson No.4.
If you are ready to start at
once, please type "s." If you
would like to review the
procedure, please type "p.n
s

reichen
reichen

6ffnen
to open
-120

arbeiten
arbeiten
to work

-184

kochen
kochen
8ffnen

rauchen

arbeiten

kochen

machen

64
80

to hand- +
to pass- +
64 good
to offer- - ta
n
to open o
-56 poor
to arbltrate o - ta
y
to look o - ta
n
to work-240
Dumbkopf!
to cook- - ta
y
to boil- +
okay
-240
to open- +
hot dog
-176
to smoke- +
admirable
-112
to 1'lork- +
good
-48
to boil- +
16 very good
to make- r
80
Keep it up.

That's it. You did well. I'll
be looking forward to the next
lesson.
Fig. 1 -- Typescript of a short
illustrative lesson in which a computer
plays the role 01' instructor in languagevocabulary drill. The student typed "0"
to start the session, "s" to start the
lesson, the English words (and terminating dots) in right-hand column, and the
abbreviations of "yes" and "no" in response to the computer's "ta" ("Do you
want to try again?"). The computer
typed the remainder, including scores and
comments. The procedure is explained in
the text.

124

~IAN-MACHINE

Fig. 2 -- Parabolas displayed by computer to facilitate student's exploration
of relations between gr.aphical and
symbolic representations of mathematical
expressions.

COOPERATION

ON-LINE MAN-COMPUTER COMMUNICATION

0:'

NUl

125

NU2

NU!

EHER

OPD

ORICIN

Fig. 3 -- Oscilloscope displays of
several aspects of a projected interdepart:7_ental IIcom;nerce" pattern in a
hypothetical hospital. The upper graph
shows the anticipated time distribution
of patient transport trips to the X-Ray
Department. The lower graph shows the
conditional distribution of those trips
among departments of origin.

MA~-MACHINE

126

,.................................................................................................:

I . .,. . . . . . .~.~~.:. . . . . . . . .
!i

.L~

i
i

.. j (VERTICAL
. ! TRAVEL
. ! 'ATMI)

1
:

..T~:

I :.. . ·. . ·. ·........·. . ·......1
i,·;~

('H~R"ACY)

.......... , , .

.;~.~x.; ~. :~. ~!...:.

!.:. :.:. :. :...:

FLOOF.:

('ART IAL PLAN

:.1

Fig. 4 -- Oscilloscope display of an
outline planning sketch of one floor in
a hypothetical hospital.

INTERDEPARTMENTAL COMMERCE
FOR R PROJECTED COMMERCE
PATTERN AND HOSPITAL PLAN
1000i ..

900~,

···r\\

~ 700;..
N
:

all;..

~ :::::

til
Y

/"'"

\~-_///---..

' .." " "

"~---...--,

....

200!"
1 00;"

.
.
.
.
0: .. ·· .. ···· .. ·· ...... · .. ····: .... · ...... · .... ····· .. ···: .. · .. ··· .. · .. ··· .......... : .......................... :
P-A T T Rtil NS P
.. E 0 I Ctil L
SUP PLY
P E ~s 0 NAL I N F 0
TASK

Fig. 5 -- Oscilloscope display of the
performance, in respect of "commerce,lI
of a proposed hospital plan. Scale time
is defined as man-minutes spent in
transit. The contributions of
individuals to this quantity are weighted
by coefficients associated with their
personnel categories.

COOPERATION

127

ON-LINE MAN-COMPUTER COMMUNICATION

~3'

?~o;~~rap~3

::"splays

~:.ade

ext for

::"n~erpretation.

:SC~::OSCO;_~

ty Prc::;:>a:r Jr&.ph.

Sec:;

MAN-MACHINE COOPERATION

128

Fig. 7 -- Photograph of oscilloscopic
display made by Memory Course. See text
for interpretation.

129

SOLUTION OF NONLINEAR INTEGRAL EQUATIONS
USING ON-LINE COMPUTER CONTROL
Glen J. Cullero and Robert W. Huff 00
Ramo-Wooldridge, a Division
of Thompson-Ramo-Wooldridge, Inc.
Canoga Park, California

Sunnnary
Experiments have been carried out using online control of a digital computer to obtain
solutions for certain non-linear integral equations. The computer program did not anticipate
any particular method of solution; each user constructed his own method during the solution procesS. Easy cases, those for which the straightforward iteration converges, were solved with
half as many iterations. Difficult cases that
were both globally and locally divergent were
solved through careful control by the problem
solver. Photographs displaying the solution
process for two sample cases are included.
Introduction
The basic philosophy of on-line computation
is principally that the originator of the problem
shall, in a fairly detailed fashion, actually
direct its solution by the computer, thereby
bringing to bear his own inSights and knowledge
based on the problem's structure or physical
significance. To make possible an operation of
this sort requires a fairly sophisticated computer with suitable interrupt capability and a
form of input-output equipment which provides for
rapid, sophisticated displays of graphical or
numerical information from the computer, and
offers convenient means for controlling the computer's activities by easily and accurately
feeding back information to the computer in
graphical or numerical form.
A system of this type can be realized in
rr.any T,·rays. At the present time a satisfactory
version of the requisite input-output equipment
exists in the form of a Display andAnalysi~
Console (~C) developed at Ramo-Wooldridge.
*On leave from University of California, Santa
Barbara, California.

**University of California Radiation Laboratory,
Berkeley, California.
***This is a console component of AN/FSQ-27
equipment developed under the auspices of Rome
Air Develbpment Center, USAF.

For output, this console has two 17" scopes (with
resolutions of 10 3 lines in each direction) which
permit the display of line segments as well as
points. Input of information to the computer is
accomplished by means of a crosshair, whose
position changes in response to a control lever,
and whose coordinates are, on push button c'ommand, transmitted to the computer, leaving a
small cross displayed on the scope; a light gun
(photocell) which can be used to select, with
complete accuracy, any desired luminous point of
a display; a series of push buttons, each of
which calls up a sub-routine from the computer
(a subset of these have an overlay feature which
allows for conveniently changing from one problem
to another); and a set of numerical keys used for
feeding in numerical information. Using this
equipment we have begun to investigate and
explore the potentialities of on-line solution of
scientific problems, and in particular, to develop
the techniques necessary for literally carrying
out mathematical analysis at the DAC keyboard.
We report here the results of o:r;te_.Q~L9W _X:ir_~t . experimental attempts in this mode of operation.
To explore the potentialities and characteristics of on-line scientific computing, it is
clear that one must attempt to solve a variety of
suitably chosen, difficult problems. In order
that the results have a content and value beyond
a mere exercise in the use of displays, we imposed the follOwing criteria:
a.

the problem must be one which presents
real difficulties for conventional
computer techniques and mathematical

the problem must be one as yet unsolved
(for any soluble problem can usually be
solved in many ways, and the ability to
do so using a new technique may not
indicate the latter's real value); and

the problem should be one of Significance
for some area of current scientific research, that is, a problem whose solution
is of value in its own right, apart from
any interest in the methods used to
obtain it.

130

MAN-MACHINE COOPERATION

Once a problem was selected, we adopted the
addi tional gro1llld rule that the computer program
to be used should involve no mathematical or
computational methods beyond those needed to construct the basic operations of analysis, thus
requiring the user to compose his techniques at
the DAC.
The first problem selected was taken from
the Bardeen-Cooper-Schrieffer (BCS) theory of
superconductivity. It was suggested and formulated by Dr. J. Robert Schrieffer, of the University of Illinois, while a consultant to this
Laboratory, in July 1961. We will concentrate
here upon the mathematical formulation of the
problem and the techniques used to solve it. A
discussion of the phYSical sigr~ficance and interpretations of results will be published elsewhere.

be a superconductor at absolute zero.
physically interesting questions are:
a.

For given C and k, what is the largest
temperature for which (1) has a nontrivial solution? This will be the
critical temperature.

For T and k given, what is the largest
value of C which permits6,. ¥ O? On the
basis of this, one can, in principle,
predict which materials should be superconductors and which should not.

For given k, T and C, what is the shape
of the solution ~(E)? From this one
can find the density of states and
thereby explain, quantitatively, the
phenomenon of electron tunnelling·
through an insulating fiJJn separating

The BeS Integral Equation

t"\-lO

In a normal (non-superconducting) metal, an
elementary excitation or "quasi-particle",
associated with momentum p, has energy E(p),
whereas according to the BCS theory, the elementary excitations in a superconductor have energy
E(p)

~E2(p) +~(p)

The "energy-gap parameter",.6, which may be considered as a f1lllction of p, E or E, satisfies a
non-linear integral equation
m

~(E)

k \

dE' K( E, E' )A( E' )
E'

( 1)

where

and

The

superconductors.

On-Line Approach

Our method of solution, in conformity with
the gro1llld rule concerning the simplicity of the
programming, requires only that the computer,
given a trial ~(E'), evaluate the definite integral in equation (1) for a number of different
values of x. The operator then merely controls
the input in such a manner as to produce agreement between the (normalized) input and output
curves. To aid himself in thiS, the operator
can, upon pushbutton cormnand, call up "Present
Input ", the function b.( E') used in the integration on the righthand side of (l)j "Present
Output", the f1lllction ~(E) on the lefthand side
of (1) which results from the integration (normalized to agree with "Present Input" at E = 0);
and "Present In-Out Ratio", the ratio of these
two f1lllctions. Lack of agreement between input
and output is readily apparent from the DAC
display, when one is far from a solution. On
the other hand, when one is near a solution the
deviations of the in-out ratio from unity providp a vpry spnsitivp tpst.

k(E,E') = (f(E + E') + f(E'-E)-C} tanh E'/2T
with
1 - E
f( E) = "2

+ ~2

11 I
+E
E·

~he constant k measures the strength of the
attractive force between electrons which arises
from their interaction with the ionic lattice
vibrations (i.e., from the emission and absorption of phonons)j C gives the strength of the
Coulomb repulsion between electrons (relative to
the phonon induced attraction)j and T is the
temperature. The equation (1) always has the
trivial solution fl;; 0, but only for a superconductor does there exist, in addition, a nonzero solution. This is the case for C = T = 0,
i.e., in absence of the Coulomb repulsion between
electrons every material would (in this theory)

Additional features available to the operator
are the following:
a.

In addition to "Present Input", "Present
Output", and "Present In-Out Ratio", he
can call up "Past Input ", "Past Output ",
and "Past In-Out Ratio", these being the
corresponding quantities resulting from
the previous integration.

On pushbutton control, it is possible to
expand or to contract· the displayed
curves in the x or in the y direction,
by as many powers of two as desired.

SOLUTION OF NONLINEAR INTEGRAL EQUATIONS USING ON-LINE COMPUTER CONTROL

Of the two DAC 17" scopes, one is used
to display the function ~(E) while the
second one displays In.6. as a function
of ln E, thereby facilitating examination of the asymptotic behavior of
the solutions.

In addition to the sophisticated display
capability represented by the above features, an
essential requirement of such on-line operation
is the ability to give directions and input data
easily and rapidly to the computer. The former
is accomplished by means of the DAC's pushbuttons. For the latter, we have available the
numerical keys of the DAC, the crosshairs and
the light gun. The numerical keys are used to
feed in the values of the parameters C, T and
~(O) at the start of each new case.
The crosshairs provide one means of controlling the
selection of the input curve, 6. (E '). At each
stage in the solution of the problem, one has
the option of using the output from the previous
integration as input for the next. However, for
many values of the parameters (c 1 0) this process fails to converge. The alterations in the
output curve which must be carried out at each
stage in order to achieve convergence to a
solution are conveniently made by means of the
crosshairs. With the insertion of only a few
crosshair points and the use of relative interpolation, it is possible to produce the desired
changes in the output curve with '-a minimum of
labor and without gross alterations of its mathematical character. (The technique of relative
interpolation uses the curve to be modified as a
basis for the interpolation rather than using
some preselected class of functions.) In
addition to this capability of relative interpolation, the program provides the possibility
of using, as input for the next integration, any
desired linear combination of input and output
curves, over all or a portion of the domain of
the functions. Also, when starting a new case
it is convenient to have available some previous
solution as a basis for relative interpolation.
As one learns how changes of parameters effect
the solutions, relative interpolation can be
used to alter the previous solution in anticipation of the form of the coming solution.
Finally, the asymptotic form of the solution can
be obtained when it has a power-law behavior.
The light gun, when pointed at two points on
the (asymptotically) straight ln ~ vs. ln E
curve, was used to instruct the computer to
display both the power-law based on these two
points and the portion of the solution in that
asymptotic region.
Armed with this collection of very simple
techniques, the operator at the console can CDmpose remarkably powerful methods of solution.
For example, we have observed, in solving the
BCS integral equation, that on successive iterations certain portions of the curve tend to
oscillate while other parts grow or decay in a
monotonic fashion. Given the facilities

131

described above, it is quite easy to control such
behaviors by employing different strategies for
different portions of the same curve, and thereby
achieve rapid convergence to a solution. To
accomplish this using conventional computer techniques would not only require a detailed prior
knowledge of the mathematical structure of the
problem and of the properties of the solution,
but would also entail programming difficulties of
no small magnitUde. This provides a nice illustration of one of the principal advantages of the
on-line method, namely the operator's ability to
use information obtained in the course of the
solution to alter and improve the very method of
attack.
Two Examples of the Solution Process
As an illustration of the use of on-line
computation for the solution of phYSical problems,
we present here the solution of the non-linear
integral equation (1) described above for two
representative sets of parameter values.
In view of the fact that for given values of
C, T and k, equation (1) may have no solution
other than the trivial one 6 ~ 0, we specify for
each case C, T and the value of ~ at E = 0, L e.,
at the Fermi surface. We are then guaranteed
that a solution exists and, for given values of
these parameters, k comes out as a kind of eigenvalue. (One can subsequently represent the results by giving ~(O) as a function of k, C and
T so that nothing is lost thereby.)
As explained above, instead of a program in
the conventional sense, the computer has simply
a collection of sub-routines. The principal one
of these is simply evaluation of the integral
specified in equation (1), Le., given an "input"
function, the computer carries out this definite
integral for ninety-six values of E (in the
dimensionless units used here the upper limit in
equation (1) is ill = 12), rescales the resultant
function of E to agree with the specified value,
~(O), at E = 0, and thereby obtains an "output"
function. (The factor needed for the rescaling
also provides an approximate value of k.) If,
in any way, one obtains an input function which
agrees in shape with the resultant output
function, one has a solution of the integral
equation (1).
For a first illustrative case, we choose
the parameter values ~(O) = .01, C = T = O. As
initial input, we use a constant function, i.e.,
~(E)
(0). When the Iterate button is pressed,
the computer takes this input and carries out the
integration required for equation (1). (The
range of integration is divided into 1536 pOints
and requires two minutes of computation time.)
When the computer signals, via a panel light,
that the computation is finished, we press the
Present Input button and obtain a picture of the
input function, i.e., the straight line shown in
Figure 1. On pressing the Present Output button,

132

we obtain the result for the integration, also
shown in Figure 1.
At this point we elect to do a straight
iteration. We press the Iterate button and the
computer takes the result of the previous integration, i.e., the previous output, and uses it
as an input for the next integration. When this
is completed, we can call up, as shown in
Figure 2 Past Input (shown dotted), Present Input
(the same as the present output of Figure 1),
and Present Output. Since the latter two show a
general agreement, continued iteration is indicated. One more pass brings us to the situation of Figure 3 where again Past Input, Present
Input and Present Output are shown. Since the
negative peaks in the latter are off scale, we
push Contract Y which rescales the ordinate by
a factor of two, resultir~ in the display shown
in Figure 4. The Present Input and Present Output c~~~s now agree so closely as to be nearly
indistinguishable, and we therefore push the
Present In/Out key which calls up a display of
the ratio of input to output, also shown in
Figure 4. One more iteration brings us to the
situation shown in Figure 5, where Present Output
(now quite indistinguishable from Present Input),
Present In/Out Ratio and Past In/Out Ratio
(dotted) are displayed. (In general, dotted
curves are used to display results of the previous integration.) A last iteration brings us
to the excellent solution shown in Figure 6 where
the Present In/Out ratio is almost identically
equal to one. It should be emphasized, of course,
that this ratio provides a very sensitive test
for the agreement of input and output functions.
At this point, we push the Print button
causing the computer to print a permanent record
of the solution obtained. In addition, we might
wish to·have the solution at a finer scale, in
which case pushing the ExJ.;a.nd x button will
produce the desired result. Figure 7 shows the
solution at the original scaling, expanded by
one factor of two and expanded by two factors of
two. 'Phis expansion jn x cR.n- bp carripd out at
any stage during the solution process and is
frequently useful in that it allows us to work
with increased accuracy upon that portion of the
curve where there is significant structure,
ignoring the asymptotic region.
We now consider a second example, this time
with the parameter choice ~(O) = .1, T = .1;
C = . 5. To begin with, we try the same approach
which proved so effective for the previous case,
i.e., we use a constant
as an initial input.
The resultant Present Input and Present Output
are shown in Figure 8. We push the Contract Y
button in order to get the output curve on scale,
and then carry out another iteration resulting
in the display shown in Figure 9, where Present
Input and Present Output are given. In contrast
to the first case discussed, the input and output
curves show no qualitative similarity. If,
undaunted, we continue the straight iteration,
i.e., use the present output curve of Figure 9

MAN-MACHINE COOPERATION

as new input, we obtain the result shown in
Figure 10 where Past Input (dotted), Present
Input and Present Output are displayed. An
additional iteration brings us to the even more
disastrous situation of Figure 11 (Past Input,
Present Input and Present Output). Present Input
and Output at a contracted scale are shown in
Figure 12. Clearly we are not on the right track.
But, wait, look back at Figure 10. The last output is very nearly equal to the initial input,
b.(E) = b(O). These differ only by the presence
of two shallow minima.
Now if we had a linear
problem and could neglect these minima, we would
have the average of the three curves shown in
Figure 10 as our solution. With this in mind we
push the Restart with New Parameter button which
takes us back to the begirilling of the problem,
and this time use the crosshair capability to
sketch in a guess for the input function. The
crosshaired points are shown in Figure 13, while
Figure 14

ShC1;"S

the pol~lgor...al cur"tte interpolated

by the computer to go through these points
(Present Input) and the resulting Present Output
function. Contraction in y gives the display of
Figure 15. Doing one more iteration brings us to
Figure 16, where Past Input, Present Input (just
below it) and Present Output (the top curve) are
shown. An additional iteration brings us to
Figure 17, where again Past Input (dotted),
Present Input (the highest curve) and Present
Output (the bottom curve) are shown. Note that
the iteration process is definitely divergent,
since over almost the entire range the Present
Output curve lies outside the region bo~~ded by
the other two.
To render the process convergent, we instruct the computer to use as new input not the
previous output, but rather a linear combination

In the present case, we choose a value of A= 0.4,
since this will make the new input lie approximately midway between the top two curves of
Figure 17. ~ne result is shown in Figure 10 wnere
we display Past Input and Output (dotted) and
Present Input and Output. Note that Present
Input, the lower of the solid curves, indeed lies
four-tenths of the way between Past Input and
Past Output. Since the Present Input and Present
Output curve lies much closer together than Past
Input and Past Output, we are clearly going in
the right direction. The result of one more
iteration, with the same value of A , gives us
the result of Figure 19 where the input and output curves are now suffiCiently close as to make
examination of the Present In/Out ratio, also
shown there, sensible. Since the principal
deviations of the in/out ratio from unity are
associated with the zero crossings of the
solution, we now revert to a value of A= 0 in
order to correct tr~t portion of the solution as
rapidly as possible. One iteration with A= 0
brings us to the situation of ~igure 20 where
Present Output and Present In/Out ratio are
shown. (The crosshairs are also displayed, since

SOLUTION OF NONLINEAR INTEGRAL EQUATIONS USING ON-LINE COMPUTER CONTROL

in their standard position the horizontal one
provides a unit reference.) Note that the in/out
ratio has greatly improved. In Figure 21 we see
the result of one more iteration with A= O. The
in/out ratio continues to improve in general,
save in the asymptotic region where we notice
that it is again divergent, the Past In/Out ratio
being closer to unity than the Present In/Out
ratio. Since unity lies six-tenths of the way
from the latter to the former, we now choose a
value of A = 0.6 and i tera te once again. The
result, as shown in Figure 22, is an in/out ratio
which deviates from unity at only two of the
three zero crossings of the solution. Experience
has shown that the most rapid convergence is
obtained, not by leaving A fixed, but by altering
it in a suitable fashion from one iteration to
the next. In the present case, since we are interested in improving the solution near the zero
crossings, we again remove the linear combination
feature, i.e., take A = 0, thereby obtaining the
situation shown in Figure 23. An additional
iteration with A.= 0 leads to Figure 24 and we
see that because of the divergence the solution
is getting worse in the asymptotic region, and
hence we are not improving the zero crossing
situation. Observing that one now lies seventenths of the way from the Present In/Out ratio
to the Past In/Out ratiO, we iterate once more,
this time with a value of A. = 0.7, obtaining
thereby the excellent final solution shown in
Figure 25. As before, we can expand the scale
if desired, as shown in Figure 26.
The two examples above do not illustrate
the use of relative interpolation as a means for
perturbing a large amount of data with very
little input information. Figure 27 shows the
above solution with four crosshair points inserted and Figure 28 shows the resulting relative
interpolation (solid curve) as well as the above
solution (dotted). Actually, this was done to
construct an input for a new case (namely
~(O) = .1, T = .3, C = .5) which proved to be
a good first guess.
Comments
From our experience thus far there is no
question concerning the value of this on-line
approach for so-called scientific computation
problems. In computing the various curves of
physical interest in this first problem (such
as 6(0) vs. T for constant k and C) the ability
to see what was happening and then decide what
to do next proved to be both fascinating and
efficient. We were able to run through all the
cases needed for such a curve and never vary
significantly from a solution. On the other
hand, when we attempted to find our first solution in a new region of the parameter space,
it was often surprisingly difficult.

133

It is possible to attack a broad variety of
problems not of the form attempted here and to
extend our work in this direction. However, we
recognize that this form of computing is no
panacea. When problems really can be automated,
they usually should be, notwithstanding occasional
gains in efficiency. Also, within the context
of a computing center, this on-line operation
only makes sense if the main facility is otherwise occupied while the problem solver is scratching his head to decide what to do. But, finally,
we are gratified to see that certain forms of cut
and try mathematics will soon be reasonably
available on a push button basis for the practitioner of the art of classical analysis.
Acknowledgements
We wish to express our gratitude to

Dr. J. Robert Schrieffer for his insight in
formulating a problem so satisfactory to our
needs; to Dr. Burton D. Fried for his good physical intuition and enthusiasm, which were of
decisive value in solving the more difficult
cases; to Roy Sather and Robert Bolman for their
patient cooperation and help in making this
computational experiment a success.

134

:\1AN-MACHINE COOPERATION

Figure 1:

Present Input and Present Output ~(O) = .01, C = 0, T

Figure 2:

Bast Input ( ... ), Present Input and Present Output.

Figure 3:

Pa~t

Figure 4:

Pres~nt

Input ( ... ), Present Input and Present Output.
Input, Present Output, and Present In/Out.

Figure 5:

Present Input, Present Output, Bast In/Out and Present In/Out.

Figure 6:

Present Input, Present Output, Past In/Out and Present In/Out.

SOLUTION OF NONLINEAR INTEGRAL EQUATIONS USING ON-LINE COMPUTER CONTROL

Figure 7:

Present Output, Present Output with Independent Variable
Expanded by 2 and by 4.

Figure 8:

Present Input and Present Output ~(O) = .1, T = .1, C = .5.

Figure 9:
Figure 10:

Present Input and Present Output.
Bast Input, Present Input and Present Output.

Figure

Past Input, Present Input and Present Output.

Figure 12:

Present Input and Present Output Contracted -oJ'

ir. Y-~2:'e ~ti:)r..

135

136

MAN-MACHINE COOPERATION

Figure 13:

The Constant Function Y == A (0) and Five Cros sbair Points.

Figure 14:

Present Input (polygonal),Present Output (off scale).

Figure 15:

Present Input, Present Output Rescaled.

Figure 16:

Past Input, Present Input a~d Present Output.

Figure 17:

Past I~put, Present Input and Present Output (note divergence).

Figure 18:

Past Input, Past Output, Present Input (
0.,.,+-,....,~

<..A. ....

.. ..J-

J:-' ............

X = .4),

and Present

SOLUTIO::\, OF ~O::\,LI::\,EAR Ii\TEGRAL EQUATIO::\S USI::\G O::\-LI::\E CO~1PUTER CONTROL

Figure 19:

Present Input (

Figure 20:

Present Output (

A= .4),
A = 0),

Present Output and Present In/Out.
Present In/Out.

Figure 21:

Present Output ( A = 0), Past In/Out and Present In/Out
(observe tail oscillation).

Figure 22:

Present Output (

A = .6),

Present In/Out.

Figure 23:

Present Output (

Figure 24:

Present Output ().. == 0), Past In/Out ane. ?resen-c ::;:n./Ou-c
(note over-all oscillation).

0), Present In/Out.

137-

138

MAN-MACHINE COOPERATION

Figure 27:

Present Output Contracted in x by the Factor 2 and Four
Crosshair Points.

Figure 28:

Past Output a nd Present Input Showing Results of Relative
Interpolation.

Figure 25:

Present Output (

Figure 26:

Present Output Expanded in x by the Factor 2.

Figure 29:

.7) and Present In/Out.

Front V"lew of D5.s-play '3nd Analysis CO!lsole (DAC)

139

ARE THE MAN AND THE MACHINE RELATIONS?
Burton R. Wolin
System Development Corporation
Santa Monica, California
Summary
Rwnans are considered as general purpose
computers, They ask two questions of t~e
environment, ''\{hat is most likely to be the
situation next?", and, ''What do I do now?" A
research progra~ is described which seeks to
determine how, a'1d how well, h1.L~ans can answer
the former question or predict the environment.
Introduction
As environments requiring control have
become more complex, and the speeds of events
in those environments have increased, there has
been a trend to supplementing or replacing men,
or the functions they have traditionally performed, with computers.
itT e can first ask the most general question
about complex systems: What are they primarily
intended to do?

The al1.swer is that they are designed and
produced to give some measure of prediction
and control over some aspect or aspects of the
real-world environment. To accomplish this
general task they must have sensors, so that
they can obtain data from the environment.
They must also have some power to discriminate
between events of interest in the environment
and others. They must be able to analyze,
synthesize, organize, a'1d classify the data
events of interest. They must, of course, have
effectors and some control over them.
What have we described? \ole have described
a government, a business enterprise, a military
system, an air-traffic-control system, and a
biological organism. We have described in general what has recently come to be called an
"open system," that is, any system which maintains or increases its organization by feeding
off tbe environment.
("''1......... _ ....... _ _

V..L.La.J:;Jll1ct.U,

TT,.... .................. ...=:t

.. Y"

..i\..C:iJ..l..l":;UJ',

l\T-. ...... , 1

i.·n;::;wc;...L....J..,

P._Y-:r!"'R~
r" ......
' 1 TIvr'\~n+v_ ... _.-.......
.J.,;'-

ed out that a complex of men and hardware performing a complex task could be likened to an
organism; that such system grows organization
and learns from and adapts to its environment.
Chapman et al.studied the manual airdefense system, which was a system where men
were the central conponents. They performed
all of the significant operations in the system.
They discriminated, claSSified, and calculated.
They figured out what the situation was and
what to do about it.

This manual air-defense system was also,
interestingly, one of the first systems which
became inadequate to cope with the increaSingly
complex, fast changing envirornnent. The system
was modified, in two stages; first, to employ
a special-purpose computer to aid the control
function, and second, to employ a generalpurpose computer to aid in the performance of
the system functions generally.
The supplementing or replaCing of me~ by
computers has been forced upon us so fast that
occasionally some unease is felt about the
whole process. In many ways we were neither
ready, nor prepared, for this development.
There are many statements made, based on
traditional beliefs, about what men can and
cannot do, or about how they should and should
not be used. These statements lack a basis of
evidence and are quite impreCise.
It is well known that given enough time,
and a problem which is not too complex or too
impreCise, men can do a respectable job of solving such a problem. Exactly what the relations are between enough time, amount of complexity, and degree of preCision are not known.
All we have really said is that men have limitations. We also know amazingly little about
how men do solve problems, make deCisions, and
perform in general high-level intellectual
functions. We do have a set of terms for the
sort of activities men engage in in some fashion when they are engaged in high-level intellectual pursuits. Some of these terms have
already been used earlier, like analyze, synthesize, organize, and classify. Close inspection of such terms and their definitions
is unsettling. More questions are raised than
answered.
Just one example of a statement based on
traditional beliefs about men, and how careful
inspection of the statement led to unanswered
...... "r.!t.1t""+4'"'net
':l1..oL
...... u V.J,.."-".LJ.U

0,..,,;1

~..a.'-4.

t::t

.......

nr1'"ov-om
l:" .... - 0.... "-"oIL.L.a.

'Y'\ .....

"f'
..,...oC!oo.,..."..h
_ . . . . . . . . - - - - _ ...... ,

m; CTh+.
............. 0 ...........

helpful.
The statement: Men learn from experience.
?ne consequence: The important decisions in
systems must be made by men. The analysis:
l.

How is the importance of a decision
measured?

What do men learn from experience?

3·

How does the type of experience a
man has influence or determine how

MAN-MACHINE COOPERATION

140

much and what is learned?

4. What are the measurable characteristics
of men which influence how much and
what will be learned from (particular)
experiences?
One cannot go to a book and get the answers
to these questions. Later, a research program
will be described which is intended to help answer some of these questions.
Some system designers have decided that the
best way to deal with man's limitations or what
man cannot do is to eliminate him insofar as
possible from a system. They attempt to design
completely automatic functions to be performed
wholly by the computer. To the extent that any
such attempt fails, which sometimes happens, man
is used as backup: The function becomes "semiautomatic. U It is frequentl:r f01.L.Y}d, hes not lead to the preferred luminosity function directly becaus e of the nonlinearity of the
intensity-response relation ..
The data in Fig. 3 indicating the relationship between the stimulus amplitude and resp·:::>ns e is found to be a power function of the
following form:
Respons e = k Stimulus· 53
(For values above threshold and below saturation) where k is an arbitrary constant dependant only upon the units used. A power function of the same general form is used by
S. S. Stevens (1961)12 and his collegues to describe magnitude functions of many sense modalities in man. More specifically, the exponent
of the power function for the crayfish caudal
photoreceptor is very close to their measures
for visual magnitude estimates of small stimuli
in the dark adapated human eye. For larger
stimulus patterns, the exponent is lower and we
suggest that this lowering is an effect of the

THE CAUDAL PHOTORECEPTOR OF THE CRAYFISH: A QUANTITATIVE STUDY OF RESPONSES

reciprocal inhibitory interactions described by
Kuffler {l952)7 for the vertabrate and Hartline
and Ratliff (1957)3 for the invertabrate visual system.s. Since the reciprocal interactions are m.inim.ized in the m.easurem.ents we m.ade (only a single cell was found on each side of the nerve cord)
a point source experim.ent and our diffuse stim.ulus experim.ent are equivalent in the crayfish and
we feel our results, therefore, reflect predom.inantly photochem.ical phenom.ena.
This analysis lends further support to
Stevens' suggestion that it is the transducer which
is responsible for the "com.pression" function
rather than som.e central learning phenom.ena as
proposed by Warren and his collegues (1958). 17
Our conclusions also em.phasize the significant
role that peripheral processing can play on perc eption by accounting for a com.plex psychophysical function exclusively in term.s of the peripheral transform..
Now, since we are in possession of both the
stim.ulus response function and the constant energy spectral sensitivity function, it is possible to
correct the obtained spectral effectivenes s curve
and develop the desired lum.inosity curve by defining a new value of the respons e Recalled R c ' the
corrected response, according to the following
rule:
1

.53
Rc = kRo
where k is an arbitrary constant. The curve slxwing the relationship between response and stim.ulus wavelengths is then in a form. com.parable to
the absorption spectrum. and psychophysical sensitivity data so elegantly used by Wald and Brown
(1958)15 to dem.onstrate the photochem.ical basis
of hum.an vis ion.
These corrected data were then norm.alized
by dividing their values by the value at 500m.p.,
the wavelength of m.axim.um. response, and plotted su~erim.posed (in Fig. 8) upon Wald & Browns
(1958) 5 com.parison of the hum.an rhodopsin absorption spectrum., the hum.an lum.inosity curve
theoretically corrected for ocular transm.ission
and finally, the hum.an lum.inosity curve experim.entally determ.ined for aphakic subjects. It can
be seen tha.t the relatiunship is extrem.ely close
for all four curves. A slight discrepancy exists
near 460 m.illim.icra which is sim.i1ar to that
found by Wald (1951)14 in a com.parison of frog
rhodopsin and the hum.an aphakic lum.inosity
curve.
Wald and Hubbard {1957} 16 recently investigated the absorption spectrum. of rhodopsin extracted from. the com.pound eye of the lobster and,
interestingly enough, their m.easurem.ents differ
considerably from. our data even though the lobster and the crayfish are closely related decapod
crustaceans.

163

The sim.i1arity between the crayfish spectral
response and that of the hum.an visual system.,
coupled with the sim.ilarity between the stim.uIus response power functions, suggest that there
is a very sim.i1ar photochem.ical m.echanism. operating in each case. However, th.e difference
between the tem.poral properties of the two m.ust
not be overlooked. The difference is so great,
varying from. tens of m.illiseconds in the vertebrate eye to six or seven seconds in the caudal
photoreceptor, that a significantly different mechanism. is suggested for the spike potential generation process. Thi s difference m.ay be related to the site of action of the generator potential or som.e other phylogenetic difference in
neural structure rather than a photochem.ical
effect and does not, therefore, vitiate the photochem.ical sim.ilarities described above. Future
research will be required to unravel the interacting physiological m.echanism.s of photochem.ical transduction, the generator potential and the
resulting pulse encoding process.
It is clear, however, that the sim.ilarities
which do exist offer the experim.enter an alm.ost
novel opportunity to explore som.e properties of
hum.an vision, both physiological and psychological, in a highly reduced m.odel preparation.
Sum.m.ary
The dynam.ics of the caudal photoreceptor
of the crayfish are extrem.ely well suited to experim.ental inquiry because of the sim.plicity of
the system. o This study has attem.pted to explore
certain of the functions m.ediated by this sensor
and to integrate these results into the fram.ework from. adjacent disciplines. Progress has
been m.ade in the following areas:
1. The stim.ulus-intensity response -am.plitude relationship was shown to fit a power
function of the following form.:
Response = K stim.ulus .53
This is strikingly close to 1hat recorded by
other investigators for the analogous hum.an
psychophysical study.
2. The spectral sensitivity curve was determ.ined for an equal energy stim.ulus spectrum.
and corrected by m.eans of the stim.ulus respon;e
relation which we have found to be a power function. The data could then be superim.posed upon
equivalent values for hum.an rhodopsin absorption and visual sensitivity with only a slight discrepancy in the shorter wavelengths.
3. A considerable difference was noted between the long tim.e constants of adaptation and
latency observed in the crayfish caudal photoreceptor and the analogous m.ore rapid m.easurem.ents in other invertebrate and vertebrate
photorec eptor s.
4. The nature of the responses to photic

164

DATA ANALYSIS AND MODEL

stimulation suggested that there are only two
neurons conducting coded information about light
intensity from the sixth ganglion.
5. Because of the similarity in the power
function relating stimulus intensity with response
level and the similarity of the spectral sensitivity curve, it is suggested that there is a similar
or even common photochemical mechanism underlying the response of both the hUITlan eye and the
crayfish caudal photoreceptor. Because of the
dissimilarity between the temporal characteristics, a different mechanism of spike action potential generation is suggested. Further res earch
is nec essary to completely analyze the interrelations between transduction, code generation and
transmission.
References
1) Cox, D. R. & Smith, Wo L. On the superposition of renewal processes.
Biometrika, 1954, 41, 91-99.
2) Gerstein, G. L. & Kiang, N. Y -So An approach to the quantitative analysis of electrophysiological data from single neurons.
Biophysical Journal, 1960, 1, (1), 15-28.
3} Hartline, H. K. & Ratliff, F. Inhibitoryinteraction of receptor units in the eye of limulus. J. General Physiol., 1957,40, 357376.
4) Hichar, J. K. Pulse height analysis of spontaneous activity in the crayfish nervous systern. Medical Electronics, Proceedings of
the Second International Conference on Medical Electronics, 1959.
5) Kennedy, D. Responses of a crustacean
photoreceptor. (Abstract)
Federation Proc., 1957, 16, 710
6) Kennedy, D. Responses from the crayfish
caudal photoreceptor.
Am. J. Opthal., 1958, 46, 19-26.
7) Kuffler, S. W. Neurons in the retina: organization, inhibition and excitation problems.
Cold Spr. Harb. Symp. Quant. Biol., 1952,
17, 281-292.
8) McAlear, J. H., Camougis, G. & Thibodeau,
L. F. Mapping of larg e areas with the electron microscope. Biophys. Biochem. Cytol.,
1961, 10, 133-135.
9) Prosser, C. L. Action potentials in the nervous system of the crayfish. II. Responses
to illumination of the eye and caudal ganglion.
J. Cell. Compo Physiol. , 1934, 4, (3), 363377.
10) Stark, L. Transfer function of a bi ological
photoreceptor, Wright Air Development
Center Report 59-311, 1959.
11) Stark, L. & Hermann H. To Transfer function of a biological photoreceptor. Nature,
Lond., 1961, 191, (4794), 1173-1174-.--

CO~STRUCTIOl\

IN THE STUDY OF THE NERVOUS SYSTEM

12) Stevens, S. S. The psychophysics of sensory function, in Sensory Communication
(Walter A. Rosenblith, ed) 1-33, The Mo 10 T.
Press & John Wiley & Sons, Inc., New York,
., nL"1

.L 7U.L.

13) Uttal, W. R. & Roland P. A. A terminal
device for entry of neuroelectric data into
an electronic data processing machine. EEG
& Clin. Neurophysiol. , 1961, 13, 637-640.
14) Wald, G. The photochemical basis of rod
vision. J. Opt. Soc. Amer., 1951, 41,
949-956.
15} Wald, G. & Brown, P. K. Human rhodopsin.
Science, 1958, 127, 222-226.
16) Wald, G .. & Hubbard, R. Visual pigment of
a decapod crustacean; the lobster. Nature,
Lond., 1957, 180, 278-280.
17} Warren, R. M., Sersen, E. A., & Pores,
E. B. A basis for judgments of sensory
intensity. Amero J. Psychol., 1958, 71,
700-709.
18} Welsh, J. H. The caudal photoreceptor and
responses of the crayfish to light. J. Cell.
Compo Physiol., 1934, 4, 379-388.

THE CAUDAL PHOTORECEPTOR OF THE CRAYFISH: A QUANTITATIVE STUDY OF RESPONSES

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DATA ANALYSIS AND MODEL CONSTRUCTION IN THE STUDY OF THE NERVOUS SYSTEM

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THE CAUDAL PHOTORECEPTOR OF THE CRAYFISH: A QUANTITATIVE STUDY OF RESPONSES

167

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THE CAUDAL PHOTORECEPTOR OF THE CRAYFISH: A QUANTITATIVE STUDY OF RESPONSES

169

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171

A THEORY AND SIMULATION OF RHYTHMIC BEHAVIOR
DUE TO RECIPROCAL INHIBITION IN SMALL NERVE NETS
Richard F. Reiss
Librascope Division
General Precision, Inc.
Glendale, California

Summary
On the basis of a specific conceptual model of
signal processing in neurons, together with some
fragmentary arguments and evidence in physiological literature, an elementary theory of a
"multivibrator effect" producible by reciprocally inhibiting neurons is developed. The results of exploratory simulation experiments are
described, and speculations on the possible role
of the multivibrator effect in semiautomatic
muscle control systems are presented.
Introduction
The investigations reported here constitute
one phase of a continuing study of small nerve
nets. The most highly developed nervous systems
contain, and are built upon, more primitive subsystems, each of which is responsible for basic
units of behavior. These subsystems are to some
extent autonomous but must also act in cooperation with each other within a hierarchical framework. Although an understanding of the hierarchy
as a whole may be the ultimate objective. such
understanding can scarcely be more than superficial unless and until the capabilities, the
demands and dependencies, of the parts are known
in some detail.
Thus the repertoire of behavior that can be
produced by small groups of neurons is an important problem both for the biologists and psychologists who seek to understand complex nervous
systems for their own sake, and for those of us
who are motivated by a desire to eventually synthesize inferior, equivalent, or perhaps even
superior machines. As empirical data accumulates,
particularly in recent years, the picture of an
individual neuron becomes ever more complicated.
In the face of this physiolo~ical evidence. it is
increasingly difficult- to ju~tify the char;cterization of a single neuron's signal-processing
capabilities by such concepts as simple logical
elements. And consequently our views of the
potential behavioral range of small nerve nets
must be correspondingly expanded.
The theory and simulation experiments discussed in this paper all revolve around the rhythmic
behavior that might be produced by just two neurons which inhibit each other, a case that does
not look very promising at first glance. The
conceptual and simulation models of neural signal
processing used are also rather simple. Nevertheless, the expenditure of considerable time and

effort investigating the basic neuron couplet has
produced what could only be called exploratory
results. An exhaustive, definitive study has yet
to be carried out. The possible functions of
such couplets when connected with a few other
neurons, sensors, and effectors are only touched
upon here. It is clear that we have done no more
than scratch the surface of that problem. And
finally, a methodical correlation of our results
with existing physiological data and attempts to
predict future empirical discoveries have only
just begun.
A secondary but important objective in this research is the comparative evaluation of analog and
digital simulation techniques for the study of
small nerve nets. We believe that in the long run
the development of powerful simulation tools will
prove crucial to the advance of nerve net theory.
However, that subject is beyond the scope of this
paper and receives only casual mention. The section describing briefly the analog and digital
models is included primarily to provide other investigators a basis for comparing their results
with ours. The reader may well wish to skip from
the description of our conceptual model to the
section on reciprocal inhibition theory.
A Conceptual Model of the Neuron
The digital and analog simulation models used
in these studies are based on a simple conceptual
model of signal processing in neurons. This conceptual model has few if any novel aspects when
compared to those underlying previous simulation
models. The emphasis on "fatigue" is somewhat
unusual, but the functional effects of fatigue are
similar to those of "adaptation" as employed, for
example, by Harmon 8 ,9 and Taylor 17 in their analog models.
It will be assumed that the state of a neuron
at any particular moment is completely defined by
the values of three state variables S, ~. and E.
The value of S represents a quantity of "stimulant" produced by pulses from other neurons, i.e.
by all previous inputs. For a given set of parameters, S has a maximum possible value Smax and
a minimum possible value Smini Smax is a positive number, and Smin is a negative number. An
"excitatory" input pulse raises S toward Smax,
whereas an "inhibitory" input pulse decreases S
toward Smin' As a consequence of these limits
on excursions of S, we obtain a process resembling "defacilitation" in real neurons. As S
approaches Smax, excitatory inputs lose their

172

DATA ANALYSIS AND MODEL CONSTRUCTION IN THE STUDY OF THE NERVOUS SYSTEM

effectiveness regardless of pulse magnitude.
The same applies to inhibitory inputs if 8 is
driven negatively toward 8 min. Initially 8=0,
and in the absence of incoming pulses 8, whether
positive or negative j decreases exponentially to
zero with the passage of time.
The state variable 8 corresponds roughly to
the degree of polarization in a synaptic membrane.
When 8=0, it represents the normal resting potential across the membrane. Positive excursions
of 8 represent depolarizations, and negative excursions represent hyperpolarizations. However,
a neuron receiving pulses from two or more axon
terminals may have two or more distinct synapses.
In this situation 8 represents the combined effects of all synaptic membrane states at that
point in the neuron where new pulses are generated, i.e., where the neuron "fires" and initiates
a pulse which propagates out along its axons to
other neurons. Hence the spatial and temporal
summation of all inputs to the neuron are represented by the lumped variable 8.
It is assumed that each input pulse has associated with it a number which characterizes its
nature (excitatory or inhibitory), the axon terminal at which it appears, and the spatial and
temporal degradation of the resulting synaptic
response which occurs within the neuron between
the synapse and the locus of firing. An excitatory input pulse is represented by a positive
number; an inhibitory pulse, by a negative number. These numbers will be called "terminal coefficien ts" because they will be assumed to be
the same for all pulses arriving at a particular
terminal. Thus each axon terminal is assigned
its coefficient, and this number will then characterize all pulses passing through that terminal and the corresponding synapse.
This conceptual model focusses attention on
that small area in a neuron where new pulses are
generated, i.e., the "spike initiation locus."
The three state variables 8, 8, and E are actually assumed to describe just the state of the
spike initiation locus; but since we are not concerned here with the complexities of intraneural
signal interactions, we shall continue to use
these variables to represent the state of the
neuron as a Whole. As a consequence of this
drastic simplification, two other assumptions
are introduced. First, all pulses are of very
short duration and resemble axon spikes in form.
The "ballistic effect" of a synaptic membrane,
which smears an incoming axon spike over a considerable time interval, is ignored. An incoming
pulse causes an almost instantaneous change in S
(although the addition may not be algebraic due
to the defacilitation imposed by Smax and Smin).
Second, all time delays involved in the generation and propagation of a pulse are lumped into
a set of "transit times" for a particular neuron.
In effect these simplifying assumptions push axon
terminals up against the spike initiation locus
with the result that a neuron is represented by
nothing more than a spike initiation locus and a

branching axon having various transit times
associated with its various terminals.
In the simulation experiments described below,
the s;!eneration of a pulse - Le •• "firing" - has
no effect on the val~e of 8. Only incoming
pulses and the passage of time influence the
behavior of 8; there is no "resetting" of 8 subsequent to firing. This may constitute a very
serious distortion of events in some real neurons.
However~ the investigations of Eccles, Fatt, and
Koketsu on Renshaw cells in spinal ganglia and
the empirical and simulation studies of cortical
neurons by Burns l ,2 indicate that for at least
some classes of neurons the act of firing does
not wipe out the stimulating potentials and currents which cause"d firing. To our knowledge,
there have been no broad comparative studies of
the effects of varying degrees of stimulant destruction due to pulse generation.
The second state variable 8 is a "firing threshold." The most important parameter associated
with 8 is its "resting" value Sr. Initially 8=8 r •
If firing occurs (a new pulse generated), 8 is
assumed to rise to a very large value and then
decay, with the passage of time, back to its
resting value. The assumptions regarding the
type of decay are different in the digital and
analog models and will be described at the appropriate points below.
We shall define two types of hypothetical neuron in terms of the criterion for firing. A reI axation neuron fires whenever S 28. A single
strong excitatory pulse can raise 8 well above
the resting threshold Sr. causing the neuron to
fire. The threshold goes effectively to infinity
immediately after firing and then decays toward
Sr. If the decay of S toward zero is sufficiently slow and the decay of 8 toward 8 r is sufficently fast, then at some moment the threshold
will fall below the value of S, causing the neuron
to fire again. A single excitatory pulse can
cause such a neuron to generate a series of pulses
with a constantly decreasing frequency. The
electronic analogs constructed by Burns l can exhibit this type of "after discharge," and the
electronic analogs used in our studies can also
be adjusted to operate in this "relaxation mode."
For our purposes, the most important feature of
a relaxation neuron is that it can generate pulses
which are not synchronous with excitatory input
pulses. Its firing frequency can differ greatly
from the frequency of excitatory input impulses.
Clearly, a relaxation neuron may have an output
frequency many times greater than the input frequency and thereby act as a "frequency amplifier."
This type of behavior appears to have far-reaching
consequences for nerve-net theory in general, but
the subject will not be pursued here.
The digital simulation of a relaxation neuron
presents a messy~ costly problem, particularly if
a small computer is used. Each time an excitatory
pulse arrives or the neuron fires it becomes

THEORY AND SIMULATION OF RHYTHMIC BEHAVIOR DUE TO RECIPROCAL INHIBITION IN SMALL NERVE NETS

necessary to calculate whether and when i will
next fall below 8. If neither 8 nor i decay in
a linear fashion, the simultaneous solution of
the functions governing 8 and i decay will generally require time-consuming iterative computations. To avoid such complications in our
digital simulation model, a somewhat more crude
conceptual model of neural firing was postulated.
A coincidence neuron fires at time t if and only
if: (15 a pulse arrived at time t, and (2) 829
after this pulse has acted on 8. Thus a coincidence neuron can fire only at those times when
input pulses (whether excitatory or inhibitory)
arrive. This model requires the simulation program to test for firing conditions (S~i) only
when input pulses are present, and the prediction problem is eliminated.
Obviously, a coincidence neuron must fire at
frequencies which are the same as or subharmonics
of the input frequencies. This model corresponds
to a real neuron which responds to both the absolute magnitude and rate of change of stimulating potentials or currents. We shall not speculate on the existence of such real neurons here
because comparative simulation experiments (discussed below) indicate that the basic reciprocal
inhibition networks constructed from coincidence
neurons behave in essentially the same way as
reciprocal inhibition networks constructed from
relaxation neurons. It is likely that other types
of network would produce radically different types
of behavior depending upon which type of neural
model is used.
The behavior 8 and i without fatigue is illustrated in Figure 1. The top graph shows the amplitude and times of arrival of input pulses
(vertical marks) from several axon terminals.
Marks above the base line denote excitatory
pulses and marks below denote inhibitory pulses.
The second graph shows the response of S (solid
line) and i (dashed line). Initially 8=0 and
i=i r • Typical values of the limits 8 max and Smin
are indicated. The first two excitatory inputs
at times a and b are of the same amplitude, but
the second is less effective due to defacilitation
A third excitatory input at time c raises S above
i and firing occurs. The generation of an output
pulse is indicated in the third graph. At the
time of firing, i rises very sharply to a very
high value and then decays back toward i r • The
interval during which i>8 max is the absolute refractory period I and this is followed by the relative refractory period during which 8max>i>iro
At times d and e inhibitory inputs drive 8 negative. Excitatory inputs at f and g raise 8 above
i, which has returned to ire The input at time h
fails to cause firing. However, this is a relaxation neuron and the decay rates of i and 8~
such that 8 falls below 8 at time i, thereby
causing a third output pulse to be generated. A
final inhibitory input at j hastens the decay of
S to zero.
If this were a coincidence neuron, it would
behave in the same way except at time i; the

173

threshold would fall below 8 for a short time,
but no firing would occur. Thus the third output pulse would be absent.
The third state variable, E, is introduced into
the conceptual model as a means for producing
"fatigue." It is intended to represent a quantity of potential energy stored in the neuron.
When the hypothetical neuron is fully "rested,"
E=Emax , a positive number which E never exceeds.
The generation of an output pulse upon firing
reduces E by some amount, and then energy flows
into the neuron from its environment raising E
back to Emax in time. It is assumed that E can
never reach zero and, therefore, always has a
positive value. The rate at which E returns to
Emax will be called the "recuperation rate,'~ and
the amount by which E is reduced when the neuron
fires will be called the "fatigue decrement."
The value of E influences the generation of
pulses by altering the decay rate of the threshold i. As E decreases the decay rate of i decreases, thereby producing greater absolute and
relative refractory periods. As E approaches
zero the total refractory period approaches infinity. The relation between changes in E and 9
are illustrated by Figure 2. Here i=9 r and
E=Em~x initially, and it is assumed that the neuron ~s of the relaxation type. In order to simplify the discussion, 8 is suddenly raised above
ir at time a and maintained somehow at a constant
value until shortly after time g (as indicated by
the dashed line). The upper graph shows the behavior of 8; and the lower graph, the corresponding behavior of E. At time a, firing causes E to
be reduced by the fatigue decrement. Between a
and b the recuperation process raises E back toward ~ax' but the decay of 9 to S is so rapid
that firing occurs before E is fully recuperated.
Each time the relaxation neuron fires the value
of E is further reduced and the decay rate of 8
is thereby reduced. By time f an equilibrium has
been reached; the period between firings, as determined by the decay of i and the value of S, is
such that the fatigue decrements are just balanced by the recuperation process between firings.
This firing frequency will be called the "fatigue
equilibrium frequency." Of course, the situation
illustrated by Figure 2 is artificial because
normally 8 will be fluctuating rather than constant; the interactions of 8, i and E become quite
complex, and an equilibrium may never appear.
Our use of the term "fatigue" in these conceptual and simulation models should not be taken too
seriously, but it seems more appropriate than
"adaptation'·' because E is affected by the generation of pulses (with the presumed expenditure of
considerable energy) rather than the arrival of
input pulses. Adaptation is usually defined in
terms of the response of sensory neurons to relatively steady "generator potentials" and is attributed to repolarizing processes in synaptic
membranes. In our conceptual model this would be
represented by some process acting on 8, either
self-induced by the value of 8 and/or caused by

174

DATA ANALYSIS AND MODEL CONSTRUCTION IN THE STUDY OF THE NERVOUS SYSTEM

firing. The process might take the form of a
gradual increase in the decay rate of 8 as a
function of the mean value of 8 over some time
interval. It may be noted that Taylor 17 introduces an "adaptation network" into his neural
analog only when the model represents a sensory
neuron subjected to steady generator potentials,
and that the network is inserted in the excitatory input section where it is unaffected by
firing and does not influence the threshold.
Brazier 3 summarizes the major behavioral differences between adaptation and fatigue in neurons as follows: (1) adaptation develops and
disappears more rapidly than fatigue; (2) anoxia
hastens fatigue but has little effect on adaptation; and (3) an adapted neuron will respond
quickly to changes in stimulus intensity whereas
a fatigued neuron respond~ sluggishly or not at
all. In regard to item 1, our conceptual model
can approximate the rapidity of onset and disappearance of adaptation if large fatigue decrements and recuperation rates are postulated.
Item 3 describes a behavioral difference that can
be spanned in our conceptual model by adjustment
of parameters. particularly input pulse magnitures,
8 max , decay rate of 8, and the algorithm governing 8 decay as a function of E.
In brief, the use of the term "fatigue" in our
conceptual and simulation models is to some degree arbitrary since "adaptation" can be approximated by suitable assignment of parameters.
Digital and Analog Simulation Models
The foregoing conceptual model of neural behavior provided the basis for designing a digital
simulation model and an electronic analog model.
Although the simulation models differ in several
respects, they both provide a satisfactory physical realization of the conceptual model. The
digital and analog models of neurons will be
called "elements" in order to clearly distinguish
between the abstract, conceptual picture of a
neuron and the corresponding physical models.
The Digital Simulation MOdel
The programmatic techniques used in the digital
simulation model are based on those used in previous studies. ll ,13 The program has been coded
and operated by Miss Alice Opolak. A small computer, the RPC 4000, has been used throughout the
digital simulation studies reported in this paper.
The program admits up to 32 elements and as many
output terminals per element, and four simulated
"pulse generators" which provide controlled stimuli to networks of elements. A simulation "run"
is initiated by reading in a description of elements desired, their connections and parameter,
and an agenda governing the frequencies of pulse
generators during the entire run. The pulse
generators are independent of each other and
their frequencies can be incremented or decremented

automatically at any prescribed points during the
run. Once the simulation program is activated,
it continues until a specified amount of time in
the nerve-net has been simulated. Two types of
output are available and are printed out on-line:
a list of every impulse generated by the elements
(ordered by time of firing) and, at selected
points during the run, a spectrum of periods between firings for each active element.
As noted previously, the elements simulated by
the digital program represent coincidence neurons,
a simplification dictated by economic considerations. The state variable S is associated with
the parameters 8 max , Smin, and a decay rate R.
Each output terminal has its terminal coefficient
hi which represents the amplitude of all pulses
emitted by that terminal. If the terminal is excitatory, then h is positive; if the terminal is
inhibitory, then h is negative. If an excitatory
terminal emits a pulse: S in the post-synaptic
element is instantaneously raised to a new value
S· according to the rule:

S•

S +

h .(Smax
Smax

-8)

Since the bracketed fraction approaches zero
as S approaches Smax, defacilitation occurs with
increasing values of 8. For all excitatory terminals, h < Smax.
In computing the response of S to an inhibitory
pulse (h c and
b > d. All four parameters, a, b, c, and d, are
inversely proportional to the fatigue rate.

An Elementary Theory of Rhythmic Behavior
Due to Reciprocal Inhibition
How might a steady stream of pulses cause and
control rhythmic bursts of activity in neurons
and/or muscles? This basic question motivated the
simulation studies reported in this paper. Reflexes provide some of the best examples of rhythmic behavior, and the problem was succinctly
summarized in 1932 by Creed et al as follows 4 :

176

DATA ANALYSIS AND MODEL CONSTRUCTION IN THE STUDY OF THE NERVOUS SYSTEM
15

"Alternating reflexes have the feature that the
the direction of movement holding for a
phase in one sense is followed by a phase
of opposite direction and this in turn by
reversion to the earlier phase, and so on,
the alternation proceeding under continuance of the same unaltered stimulus. Some
of the alternating reflexes are of irregular
alternation, e.g. the release reflex of the
foot, the pinna reflex. A number of them
are, however, regularly rhythmic, e.g. stepping. the scratch reflex, the shake reflex
of the body, the shake reflex of the head,
the to-and-fro snout reflex, biting reflex
of lower jaw. In these, the movement proves
to be not merely the alternate contraction
and relaxation of a single prime mover or
set of such; it is operated by alternate
contraction of two opposed sets of prime
movers, contraction in the one alternating
with contraction in the other. The problem
is how, under continuance of unaltered stimulation, does the initial contraction,
e.g. of the flexor, instead of persisting
during the maintained stimulus, die out
despite that stimulus, and why, as it does
so, does contraction of the extensor occur
in its stead, again then to give way to
flexion, and so on?"
Creed et al present a list of empirical data
which show in some detail various features of
alternating reflexes. Although they were working
at a rather gross level, several of these items
are of importance to our theoretical development
and deserve summarizing: (1) An alternating reflex may continue to operate in the absence of
afferent feedback from the limbs involved; (2)
During the relaxation phase, a muscle (or synergetic group) may receive no excitation whatever,
i.e •• the motor neurons are cut off entirely; (3)
"The turning point is not abrupt, ••• each phase
presents a regular waxing and waning of activity";
(4) "It is noteworthy that the scratch and stepping (reflexes) are facilitated by as~hyxial conditions"; (5) "The self-generated proprioceptive
stimuli of the muscles which take part in (the
alternating reflex) can regulate the act but are
not essential to its rhythm."
Item 1 suggests that the rhythmic excitation
does not stem from some feedback loop through afferents and therefore probably originates in the
central ganglion. Items 2 and 3 indicate that
while the switchover from one muscle to its antagonist is not instantaneous it does go to completion; i.e., excitation to one muscle is mostly, if
not entirely, cut off. Item 4 is particularly important because, as noted previously, lack of oxygen hastens fatigue while it has little or no
effect on adaptation. Hence if we are confronted
by a choice between fatigue and adaptation in explaining the alternating mechanism, fatigue is to
be preferred. Finally, item 5 indicates a useful
role of afferent feedbacks in regulating the alternating mechanism.

In his classic work of 1906, Sherrington discusses what he calls "reciprocal inhibition" by
which he means " •••• the inhibition at one part
always appears as the negative aspect of positive
excitation at another." This is a very general
definition; apparently Sherrington's "part" may
be anything from a single neuron up to a whole
segment of the nervous system together with its
associated muscle groups. He generally uses
"reciprocal inhibition" to describe, rather than
explain, the behavior of various reflex systems.
However, in discussing alternating reflexes he
quotes at length a theory, proposed in 1903 by
McDougall'; wherein reciprocally inhibiting chains
of neurons are used to explain the rhythmic alternations of contraction and relaxation. The network in Figure 4 is equivalent; using our diagrammatic conventions, to the network analyzed by
McDougall and Sherrington& The topology is somewhat different due to their use of a now-defunct
theory of inhibition at synapses. Arrowheads
stand for excitatory axon terminals and solid circles for inhibitory terminals. McDougall argued,
in effect, that if al is more active than bl, then
the net stimulus to a2 will be excitatory whereas
the net stimulus to b2 is inhibitory. Hence b2
will be cut off while a3, a motor neuron, will be
active and cause the flexor to contract. After a
time, "fatigue" will raise the synaptic resistance
of a2, thereby lowering its activity and indirectly
removing some of the inhibition at b2 so that it
becomes more active and, in turn, suppresses a2.
This would provide a switch of excitation from a3
to b3 with a subsequent relaxation of the flexor
and contraction of the extensor.
However, McDougall failed to recognize the possibility of alternately achieving excitation and
inhibition of a3 and b3 when the inputs to al and
bl are of equal strength. He assumed that al and
bl must be stimulated at different intensities.
Furthermore, he was primarily interested in the
possible role of reciprocal inhibition in the visual apparatus of humans; and he carried out a
variety of experiments on edge effects and related
phenomena which supported his thesis to some extent. It is interesting that such contemporary
theorists as Fessard6 and Taylor 16 assume, as did
McDougall, that the major function of reciprocal
inhibition in vision is to amplify and sharpen the
edges of figures projected on the retinal matrix.
The key ideas here are those of "reciprocal inhibition"--neurons inhibiting each other--and
"fatigue." Combined, these ideas suggest an explanation of certain types of switching action. To
our knowledge. McDougall's is the earliest clear
theory of this type. Although the theoretical and
simulation studies reported here stemmed by analogical reasoning from the behavior of freerunning electronic multivibrators (a device unknown
to McDougall and Sherrington), the ideas are essentially the same and McDougall clearly set the
precedent.
In order to develop the theory of reciprocal
inhibition further, we shall first concentrate on

THEORY AND SIMULATION OF RHYTHMIC BEHAVIOR DUE TO RECIPROCAL INHIBITION IN SMALL NERVE NETS

the simplest conceivable network. as shown in
Figure 5. and ignore its possible role in a larger
system. The parameters of neurons a2 and a3 are
ap~roximately symmetric in value.
The firing frequencies of al. a2, and a3 will be denoted by fl,
f2, and f3, respectively. We start with the naive
assumption that the effective stimulation provided
by an axon terminal of any neuron is the product
of that neuron's firing frequency and the amplitude of the pulses characteristically produced by
the terminal. If the terminal is inhibitory. it
generates a negative stimulation. Let the excitatory terminals of neuron al produce pulses of the
same amplitude, namely, 1.0. The inhibitory terminals of a2 and a3 produce pulses of amplitude
h2 and h 3 , respectively. Finally, let us assume
that the firing frequency of an element is the
simple sum of all input stimulation (and let the
dimensions take care of themselves).
Thus for any given frequency fl of aI, the frequencies of a2 and a3 are given by:
(1)
(2)

Since a negative frequency is impossible, if the
right side of either equation has a negative value,
the corresponding frequency is zero. This is the
same as saying that if the net input to a neuron
is inhibitory, that neuron will not fire at all.
For a given constant frequency of aI, what will
the network do? The most obvious answer is given
by a simultaneous solution of equations (1) and
(2), which yields:

(3)

(4)

If, for example, the inhibitory terminals produce
rather strong pulses of h2
h3
2.0 (strong compared with the excitory terminals of al), then
f2 = f3 = f l /3.

But there are two other simultaneous solutions
to equations (3) and (4); namely, f2 = fl and f3 =
0, or f2 = 0 and f3 = f 1 ; if h2 and h3 are greater
than 1.0. These are legitimate solutions because
(1) and (2) are not ordinary equations. If the
left side is zero, any negative value on the right
satisfies the equality because a neuron whose net
input is negative (inhibitory) will presumably
have a frequency of zero.
Thus this simple model predicts that the network of Figure 5 can have three stable states:
(1) both a2 and a3 firing at some fraction of the
frequency of ali (2) f2 = fl with a3 totally suppressed; and (3) f3 = fl with a2 totally suppressed.

177

We shall say that in the second case a2 is dominant and in the third case a3 is dominant. Dominance implies here that the other element is
totally suppressed.
Suppose now that if a2 is initially dominant,
it gradually loses its sensitivity to excitatory
pulses from ala In effect, the amplitude of
pulses from al decreases; (1) can be rewritten as
f2 = hlfl - h3f3 where hl< 1.0 and is decreasing.
If f2 decays far enough, the right side of (2)becomes positive and a3 begins firing. Each-Inhibitory pulse from- a3 hastens the decrease in the
frequency of a2, which in turn removes more inhibition from a3, and so on. It is conceivable that
this self-facilitating process, which we shall call
"switchover", will terminate with a2 suppressed and
a3 dominant. The critical point which initiates
switchover occurs when f2 decays to f2 = fl/h2,
which is the "switchover threshold." Similarly,
there is a switchover threshold for a3i namely,
f3 = fl/h3.
Therefore, on the basis of this model of neural
behavior, a2 and a3 can become alternately dominant
if each neuron loses its sensitivity as a result of
repeated firing but regains that sensitivity during
the time when its opponent is dominant.
The Multivibrator Effect
We shall call the alternating dominance of reciprocally inhibiting neurons tithe multivibrator
effect." In the aforementioned case, the sequence
of dominance would be •••• a2, a3, a2, a3 •••• etc.
The time interval over which a2 can maintain dominance is the "dominance interval" of a2, denoted
by D2. Likewise, the dominance interval of a3 is
D3. Given symmetric parameters in a2 and a3, one
should find that D2 = D3. Furthermore, the more
rapidly the dominant neuron's frequency decays, the
shorter its dominance interval. On the other hand.
since the switchover threshold is inversely proportional to the impulse amplitude at the dominant
neuron's inhibitory terminal, the stronger its inhibitory terminal, the longer its dominance interval. Consequently, asymmetric values of frequencydecay rates may, for example, be compensated by
asymmetric strengths of inhibitory terminals; and
it is possible that D2
D3 even though parameters
are ~ symmetric. But, in general, asymmetric
parameters would likely make D2 ~ D3.

These are a few characteristics of the multivibrator effect in a network with reciprocal inhibition, as predicted by the algebraic approximations
to real neural behavior. The simulation studies
were undertaken as a result of such an analysis.
Somewhat to our surprise, the predictions of this
exceedingly crude algebraic model turned out to be
quite good in respect to modes of behavior and the
general effects of varying the several parameters.
Exact quantitative comparisons were not possible
because the digital and analog models are much more
complex than the neurons assumed by the algebraic
model.

178

DATA ANALYSIS AND MODEL CONSTRUCTION IN THE STUDY OF THE NERVOUS SYSTEM

The frequency decay in the dominant neurons
which must be present if switchovers are to occur,
could s of course, be produced by either adaptation
or fatigue. Although we know of no decisive empirical evidence on which to base a choice (in
fact both could be operating), fragmentary physiological data, such as discussed above, suggests
that fatigue is more likely to be the cause of
frequency decays in dominant neurons, if indeed
the multivibrator effect ever actually occurs in
real nerve nets. To our knowledge the multivibrator effect has never been directly observed in
living nervous systems.
Simulation Experiments on Simple
Reciprocal Inhibition
The first series of simulation experiments were
carried out on the digital model. Since the elements in this model represent "coincidence" neurons s there was some reason to fear that the harmonic character of their behavior would interfere
with, if not prevent, the appearance of a multivibrator effect. A network of the type shown in
Figure 5 was the subject of these experiments.
Element al was represented by one of the simulated
pulse generators.
Initially the parameters of a2 and a3 were perfectly symmetric in values. Numerous tests over a
wide range of input frequencies with various parameter constellations failed to produce anything
more than rather synchronous firing in a2 and a3
at frequencies considerably lower than the input
frequencies. This corresponded to the mode of
operation predicted by equations (3) and (4)
above. Neither element was able to gain dominance
over the other and so the multivibrator effect
could not appear.
The next step was to introduce asymmetry into
the parameters. After only a few experiments, the
multivibrator effect did appear. The pattern of
firing shown in Figure 6 is typical of the behavior
obtained in these early, and most subsequents experiments. Here e2 becomes dominant first~ followed by a switchover to a3, followed by a switchover to a2, and so on. Inspection reveals two
types of switchover in this sample record. The
switchover from a2 to a3 does not involve any synchronous firing. The last impulse of a2 is followed by an appreciable interval before the first
pulse of a3 appears. Furthermore, a3 begins firing at the highest frequency attained during its
dominance interval, i.e., the period between the
first two pulses is as short as any in the dominance interval. The second type of switchover is
illustrated when a3 loses dominance. The last
pulse of a3 is synchronous with the first pulse of
82, but there is a long period between a2 t s first
and second spike. Of course all firings here were
synchronous with pulses from the generator ale
However, both types of switchover have been seen
in analog elements simulating "relaxation" neurons.
Hence these do not appear to be artifacts introduced by the harmonic behavior of coincidence neurons. The second type of switchover evidently

occurs when the state variables and input times
are such that the dominant element manages to get
off one final pulse just as the other begins firing. This last pulse, after the delay produced by
the elementts transit time, inhibits the onset of
firing in the newly dominant element - thus the
long period between first and second firings in the
other element.
The dominance intervals of a particular element
tend to be consistently terminated by the same
type of switchover for a wide range of input frequencies. Typically, the element having the lesser
"sensitivity" produces the first kind of switchover, which will henceforth be called a "gap"
switchover, while the more sensitive element produces the second kind, the "synchronous" switchover. A third kind of switchover, the "overlap,
is discussed below.
The decrease in frequency during the dominance
interval, due to fatigue, is quite marked in Figure
6. The input frequency is constant, but the dominant element is able to maintain its maximum frequency (which may be equal to the input frequency,
but is more commonly a subharmonic) for only two
or three firings. The multivibrator effect cannot
appear unless the fatigue equilibrium frequency is
less than the switchover threshold frequency for
the dominant element. The network of Figure 6 involves 18 parameter values in the digital model,
and we have not been able to develop any algorithms
for precise calculations of either the fatigue
equilibrium or switchover threshold frequencies.
It is not clear that the development of such algorithms would be worth the experimental effort required for induction and verification. The model
is too arbitrary.
As noted, the multivibrator effect was obtained
only after asymmetric parameter values were introduced. Many variations of asymmetry were tested
(as many as five networks were simulated simultaneously with all but one parameter held constant),
and a peculiar similarity of successful parameter
constellations appeared. Although asymmetry w~~
necessary to the occurrence of the multivibrator
effect, the asymmetry apparently must be of the
"self-cancelling" variety. For example, if the
excitatory terminal contacting a2 emits pulses
larger than those emitted by the excitatory terminal contacting a3 (which gives a2 an advantage),
then the inhibitory terminal contacting a2 should
also emit larger pulses than that contacting 83
(which tends to cancel the excitatory advantage of
a2). We have not yet found a satisfactory explanation for this phenomenon.
Three Modes of Behavior
The two-phase multivibrator effect appears only
over a rather well-defined range of input frequencies. The upper and lower limits of this range are
a function of all parameters. Outside these limits,
two other modes of behavior are commonly observed.
By setting the input frequency initially at zero
and raising it in stepwise fashion by small

THEORY AND SIMULATION OF RHYTHMIC BEHAVIOR DUE TO RECIPROCAL INHIBITION IN SMALL NERVE NETS

increments, all three modes appear in sequence.
At very low input frequencies, one element
dominates continuously. If there is mixed or synchronous firing of both a2 and a3 at low frequencies, it is unlikely that the multivibrator effect
will appear at any frequency. As a rule, it is
the more sensitive element that holds perpetual
dominance at these low frequencies. We shall not
attempt to develop a formal definition of "sensitivity" here. Because of the self-cancelling
asymmetry, it is not always possible to predict
which element is the more sensitive even though,
in the digital model, all parameters are precisely
known. But, generally, the element receiving the
largest excitatory pulses, if it also has the
largest Sma x (least defacilitation), will be the
most "sensitive" in our usage of the term.
As the input frequency is raised step by step,
a transition from one element dominance to the two~
phase multivibrator effect appears. This transition is not necessarily sharp. There may be a
small range of input frequencies over which the
multivibrator effect appears only sporadically, in
which case there is no precise lower limit of the
multivibrator range. As the input frequency is
raised further, the dominance intervals become
shorter and shorter until another transition range
is reached. Here there is a transition from the
multivibrator effect to mixed firing in both elements. In effect, the dominance intervals are
reduced to one or two pulses and the concept of
"switchover" becomes rather meaningless.
Small changes in parameters have little effect
on the input frequency range of the multivibrator
mode. A great many more experiments must be made
before a clear picture of the effects of various
parameters on this range can be put together. The
fatigue rate appears to be the most important factor in determining the lower and upper limits of
the multivibrator mode. For example, experiments
on the digital model with a certain set of parameters which produced a low fatigue rate resulted
in a frequency range of approximately 300 to 500
pulses per second for the multivibrator mode.
Holding all other parameters constant, the fatigue
decrement was doubled with the result that the
frequency range was shifted down to approximately
200 to 400 pps. Thus, for this constellation of
parameters, the magnitude of the frequency range
remained essentially constant while the lower and
upper limits were shifted do~~ward by an increase
in the fatigue rate. Experiments on both the digital and analog models have generally indicated that
the higher the fatigue rate (within limits), the
lower the input frequency at which the multivibrator effect first appears. The upper limit of the
multivibrator mode behaves in a less predictable
way.
Dominance Intervals as a Function of Input
Frequency
The curves in Figure 7 are plots of the dominance intervals versus input frequencies for the

179

two elements in a network, such as shown in Figure
5, using the digital model. The upper curve shows
the dominance intervals in the more sensitive element. The multivibrator effect appeared at about
320 pps in this experiment, and the dominance interval of the more sensitive element was approximately 1-1/2 times greater than that of the other
element. This difference is due to the asymmetric
parameters. As the upper limit of the multivibrator mode (about 450 pps) is approached, the dominance intervals become nearly equal. Each point
on this graph is the average of several dominance
intervals. As might be expected in coincidence
neurons, harmonic effects can cause the dominance
intervals to fluctuate about an average value for
any given input frequency. The analog elements,
when simulating relaxation neurons, produce very
small fluctuations, generally less than one or two
percent.
Both the shape and frequency range of the curves
in Figure 7 are typical of the experimental results
produced by the digital model. We have had little
success in obtaining the multivibrator effect over
a wide range of input frequencies. The analog elements, on the other hand, can easily produce the
multivibrator mode over much wider ranges (measured as the ratio of the upper to the lower limitsl
The curves in Figure 8 illustrate this clearly.
Here the multivibrator effect appears at about 15
pps and has an upper limit above 100 pps. The
upper-to-lower limit ratio is more than 7:1,
whereas the digital model rarely produces ratios
of more than 2:1. The absolute values of input
frequencies for digital and analog models cannot be
directly compared because of the differences in detailed behavior of the two models.
The curves in Figure 8 illustrate two extremes
in the variation of dominance intervals with increasing input frequencies. In this analog experiment, there were considerable differences between
the input and fatigue integrators of the two elements. One element (lower curve) produced dominance intervals that were almost independent of input frequency. The other element (upper curve)
was able to produce long dominance intervals at the
lower frequencies.
Effects of Transit Times
In the digital model, the delay between firing
and the appearance of impulses at the element's
outpu~ ~erminals is an independent parameter and
therefore easily controlled. In the reciprocal inhibition network of Figure 5, the transit times of
the inhibitory terminals could obviously play an
important role in the multivibrator effect. Although relatively few experiments have been carried
out to test the effects of variations in transit
times, the results point to a general conclusion
that the transit times should be small (relative to
the periods between excitatory input pulses). If
the transit times are several times larger than the
period between input pulses, the two elements have
a tendency to fire in synchronous bursts. Of
course this is an interesting phenomenon in itself

180

DATA ANALYSIS AND MODEL CONSTRUCTION IN THE STUDY OF THE NERVOUS SYSTEM

and may have physiological applications. But, in
respect to the multivibrator effect~ it appears to
be important as a contributing factor to the breakdown of the multivibrator mode at high input frequencies.
The transit times of the analog elements were
essentially zero in the experiments to date. This
may partially account for the relatively high
upper limit of the multivibrator range observed in
the analog model.
Dominance Ratios
In Figure 8, one element has a dominance inter~
val more than twice that of the other element for
low input frequencies. We shall say, then, that
the "dominance ratio" is more than 2:1 in this
case. Asymmetric parameter values are, of course,
responsible when both of the reciprocally inhibiting elements are excited at th.e same frequency and

synchronously. Dominance ratios between 10:1 and
15:1 have been achieved with ease simply by setting
the fatigue rate much higher in one element than in
the other. For a given input frequency, there is
in principle no limit to the dominance ratio that
could be obtained by: appropriate assignments of
fatigue rates. But, once the parameter values
have been set, the variation in dominance ratio
with input frequency is fixed. The dominance ratio
may be relatively constant, as in Figure 7, or may
vary considerably, as in Figure 8.
The introduction of independent excitatory inputs, however p opens up a new domain of behavior.
The network in Figure 9, which is essentially the
same as that proposed by McDougall and Sherrington
(see above), makes it possible to excite a3 and a4
at different frequencies. Thus the dominance ratio
may be influenced by outside signal sources. We
have only begun to explore this small. but significant, modification of the basic reciprocal inhibition network. The most interesting simulation results achieved to date (using analog elements)
suggest the following relationship. Let fl and f2
denote the firing frequencies of a1 and a2, in
Figure 9, and let D3 and D4 denote the dominance
intervals of a3 and a4. If for a given pair of
input frequencies the parameters are adjusted so
that D3 == D4 when fl = f2. then the dominance
ratio approximately satisfies the equation
(5)

for an appreciable range of input frequency ratios.
The fit is rough but definitely observable. If we
consider the case where a3 and a4 are driving efferent neurons, then the number of pulses during a
dominance interval is most important in determining the power developed by muscles under the control of these efferents. As a rude approximation,
we can say that the number N3 of pulses produced
by a3 during its dominance interval is proportional
to the product flD3 and similarly, for the number
N4 produced by a4. Utilizing equation (5), we
arrive at the following algorithm:

This line of reasoning su~~ests that if a reciprocal inhibition net is driving a pair of muscles,
the ratio of power developed in the muscles over a
period of time is proportional to the cube of the
input frequency ratio. Thus small differences between the two input frequencies could produce large
differences in the power developed by the two corresponding muscles.
Effects of Noise
The digital simulation program has facilities
for introducing pseudorandom fluctuations in the
frequency of a pulse generator. The operator may
specify the amount of "wobble" he desires as a
percentage of the normal period between pulses.
This may be considered a form of "noise,H and its
effects on the multivibrator mode in the single input network (Figure 5) have been tested. Wobbles
of up to 10% have been introduced without interfering with the multivibrator mode. Near the upper
frequency limit of the multivibrator mode dominance
intervals fluctuate (by a smaller percentage) because there are only three or four firings during
the interval. The wobble effect is generally insignificant because random changes in successive
periods tend to cancel out over the much longer
dominance interval.
Effects of Asynchrony
If the single input element in Figure 5 is replaced by two elements, as in Figure 9, which are
firing at nearly identical frequencies, then excitatory pulses will arrive at essentially the
same frequency but with constantly changing phase
relations. This has been tested on the digital
model with networks whose responses to a single input element were known. No appreciable effects
were observed. The multivibrator mode appears to
be quite stable in the presence of phase shifts
due to asynchronous inputs.
Overlapping Switchovers
Two types of switchover,. the "gap" and the
"synchronous," were previously noted. A third
type, which we sha1l call the "overlap," has appeared in some exp.~riments and is i1lustrated by
Figure 10. Here the dominance intervals overlap,
the fatigued element firing shortly after the newly
dominant element has become active. Although the
factors producing overlap have not been isolated
with certainty, it appears that relatively weak inhibitor terminals are mainly responsible. The phenomenon usually occurs at high input frequencies
near the upper limit of the multivibrator mode.
Rapid Changes of Input Frequency
If the input frequency is suddenly raised, it
generally induces a switchover. This effect is

THEORY

A~D

SIMULATION OF RHYTHMIC BEHAVIOR DUE TO RECIPROCAL INHIBITION IN SMALL NERVE NETS

181

most noticable in the analog model when simulating
relaxation neurons. It is most likely due to the
fact that the threshold of the nondominant element
has returned to, or near, its resting value; and
the element has had an opportunity to recuperate.
Sudden decreases in the input frequency do not induce switchovers.

by simulation for a variety of parameter constellations. If the inhibitory terminals produce
strong impulses, the switchover threshold is only
slightly below the input frequency with the result
that dominance intervals are short; and the frequency of the dominant neuron decays only slightly
during the dominance intervals.

Summary and Interpretation of Reciprocal
Inhibition Study to Date

Since the strength of muscular contraction is
roughly proportional to the excitatory frequency,
the following picture emerges: as the frequency
of a increases, dominance intervals shorten, producing a more rapid alternation of contractions;
and since the mean frequency during dominance increases, the strength of the contractions (per
unit time) increase. For any period of time considerably greater than a dominance interval, each
of the muscles is active for half of the period
(on the average) regardless of the alternation
rate. Thus the total power expended increases as
the frequency of a goes up; and as a by-product of
the characteristic decrease of dominance intervals
at higher input frequencies, the alternation rate
of muscular contraction also rises.

The study reported in this paper constitutes
only the first phase of investigations into the
possible modes of rhythmic behavior and related
switching processes in small nerve nets. It will
have become apparent to the reader that many aspects of the simplest two-element reciprocal inhibition network remain to be methodically explored.
Simulation experiments on extensions and mutations
of the basic reciprocal inhibition network (not
reported here) have already yielded distinctive,
new behavior patterns. It now seems clear that a
large variety of functions may be performed by
small nerve nets, composed of a dozen or so neurons in a few basic configurations, when coupled
with sensors and effectors. The major purpose of
this concluding section is to suggest how reciprocal inhibition in its simplest form could support
several types of semiautomatic control systems.
We have not, as yet, made a careful search of biological literature for relevent empirical data;
physiological evidence referred to here was come
upon more or less by chance. The problem is to
know what to look for in the literature, and this
knowledge will be advanced by further theoretical
and simulation studies however naive.
The most obvious application of reciprocal inhibition is the control of alternating reflexes, as
noted by Sherrington and McDougall at the turn of
the century. The rhythmic, alternate contractions
and relaxations of antagonistic muscle groups provide the fundamental means of locomotion for a
wide variety of swimming, crawling, walking, and
flying animals. Locomotion is essential to their
self-preservation. A simple neural means for producing such rhythmic behavior would have been very
desirable during the course of animal evolution,
particularly if the mechanism could be easily regulated by higher centers of a nervous system in the
more complex animals.
Let us examine the basic reciprocal inhibition
network from the standpoint of its possihle use in
controlling antagonistic muscles. The network in
Figure 11 is composed of seven neurons and two antagonistic muscles, ml and m2. Neurons cl and c2
are reciprocally inhibiting and stand between the
input neurons a, bl, b2 and the motor neurons dl
and d2. Assuming for the moment that bl and b2
are quiet, it is clear that when the multivibrator
mode is present due to the excitation of a, the
muscles will alternately contract and relax in
phase with the dominance intervals of CI and c2.
The mean frequency at which Cl fires during its
dominance intervals is proportional to the input
frequency of a. This can be easily demonstrated

If the muscles of this crude system are responsible, for example, for locomotion, then a single
stream of signals from neuron a could easily control the rate of speed produced by the relatively
more complex muscle-skeleton apparatus. It must
be presumed that if a's frequency drops so low
that the multivibrator effect disappears, the frequencies of cI and C2 are below those required for
overt contraction of the muscles. This is not unreasonable, especially in light of Hoyle's discoveries described below.
The utility of neurons bl and b2 may be simply
described if we suppose that the muscles are responsible for the rearward thrusts of opposing legs
in a crawling animal. So long as the dominance intervals of CI and c2 are approximately equal, the
path of the animal will waver about a straight
line. Its speed is proportional to a's frequency.
If now the frequency of bl rises above zero, the
dominance interval of cI will become greater than
that of c2 (with appropriate parameter values),
with the result that the average force exerted by
the left muscle will be greater than that of the
right; and the animal will slew to the right. The
greater the difference in frequencies of bl and b2J
the greater the corresponding dominance ratio, and
hence the greater the turning rate. If we suppose
that bl and b2 are sensors, a simple phobic response to external stimuli is imposed on the more
complex crawling mechanism. Not only would the
animal turn away from the stimulus, but the
stronger the stimulus, the greater the turning rate.
If both bl and b2 are equally stimulated, the toand-fro wiggling motion might provide sufficient
differences to initiate a turn.
If the frequency of neuron a or, rather, the
combined frequencies of a, bl, and b2 are so high
that the multivibrator effect is replaced by the
more or less synchronous firing in cl and c2, as

182

DATA ANALYSIS AND MODEL CONSTRUCTION IN THE STUDY OF THE NERVOUS SYSTEM

observed in simulation experiments, then contractions of the muscles would cease to be coordinated
and would tend to be spasmodic. The experiments
on transit times suggest that to obtain the multivibrator effect at high input frequencies, the
transit times should be very short and, therefore,
cl and C2 should be close together.
The foregoing flight of fancy suggests how rhythmic muscular action could be modified by external stimuli. We now turn our attention to the
regulation of the multivibrator mode by proprioceptive feedbacks. Consider the network in Figure 12. Stretch receptors rl and r2 have been
attached to the tendons of muscles ml and m2. Suppose that the dominance intervals of cl and c2 are
normally equal but the irregularities in the environment momentarily impose greater loads on muscle ml than on m2. The increased load is detected
by rl, whose frequency consequently increases.
Since it has an excitatory termianl on ci. the
dominance interval of cl will be greater than that
of C2; and so will its mean frequency. Hence ml
will be stimulated to exert greater force than m2,
and a greater fraction of the total power will be
allocated to mI. If the load increases equally on
both muscles, the dominance intervals will remain
equal, thus providing an equal distribution of
force; but the mean frequencies during dominance
will increase, thereby increasing the force of
contraction in both muscles.
The network of Figure 12 suggests how proprioceptors, by regulating the dominance ratio and
mean frequencies, permit the basic reciprocal inhibition mechanism to automatically adjust (within
limits) to varying load conditions while maintaining coordinated contractions in antagonistic muscles. Unless the loads exceed the adaptation
capabilities of the network, higher nerve centers
need not be informed of the detailed fluctuations
of loads.
It may be noted in passing that the same network might equally satisfy the control requirements if ml and m2 constitute a synergetic group
that must time-share a common load.
Recent discoveries of Graham Hoyle lO are of
particular interest within the framework of our
reciprocal inhibition studies. He has been recording the motor neuron activity in the legs of
intact locusts by means of implanted electrodes.
His recordings show that even when the locust is
at rest flexor and extensor muscles continue to
receive the alternating excitation typical of walking movements. The frequencies are too low to produce overt movement, but the pattern remains. This
suggests to us that if reciprocal inhibition is involved in the control of the locust leg muscles,
with a network somewhat like that in Figure 11,
then the lower limit of the input frequency range
for producing the multivibrator effect is well below the input frequency required for actual movement. This would ensure that if the input is sufficient to cause movement, it is sufficiently high

to produce the multivibrator effect and, therefo:2.
the coordinated alternate contractions of flexor
and extensor. Such a safety factor is consistent
with the hypothesis that a reciprocal inhibition
network could normally operate with a minimum of
monitoring from higher nervous centers.
Another discovery of Hoyle's was, to us, very
startling. He noticed that when a locust was engaged in its stereotyped "marching," the excitation to the extensor (line e) and flexor (line f)
have the patterns illustrated in Figure 13. Hoyle
hypothesizes that the movements required in marching are too rapid for the complete relaxation of
both muscles each cycle; and that, therefore, one
antagonist (the extensor in Figure 13) is continuously stimulated at a low frequency, so that it
provides a reasonably strong elastic band against
which the other muscle works. Thus more rapid
alternations are possible.
This surprised us because on several occasions,
while fiddling with the parameters of the analog
model in attempts to obtain the multivibrator effect, just this pattern of firing appeared. Of
course this was an annoying mode of behavior, being
neither the multivibrator mode nor mixed firing;
and so it received no attention. We have now returned to the simulation model in search of the
conditions which produce Hoyle's pattern consistently.
A further complication observed by Hoyle was
the periodic reversal of the pattern of excitation;
i.e., the flexor is continuously stimulated while
the extensor receives the bursts. If reciprocal
inhibition is involved, then this clearly suggests
that the fundamental pattern is caused by signal
inputs rather than inherent asymmetries in the neural parameters. The regular and distinct switchovers from one pattern to the complement suggests
the presence of a second reciprocal inhibition net
with long dominance intervals and terminals on the
fundamental net. This possibility remains to be
investigated.
The multivibrator effect could, in theory,
serve important functions in sensory perception
and internuncial communication. However, consideration of such functions necessitates the introduction of three or more reciprocally inhibiting elements and is beyond the scope of this paper.
As mentioned earlier, such theorists as Fessard6
and Taylor 16 argue that reciprocal inhibition probably serves to amplify differences in frequencies
of adjacent neurons. Burns 2 , on the other hand,
suggests that it eliminates crosstalk, the spurious
lateral spread of signals in densely packed layers
of neurons. Yet again, Granit7 supposes that reciprocal inhibition of motor neurons, whether direct or indirect, may provide negative feedback to
limit their frequencies to match the low values
ideal for exciting muscles. To our knowledge, no
theorists since McDougall have seriously examined
the possibilities of multivibrator action.

THEORY AND SIMULATION OF RHYTHMIC BEHAVIOR DUE TO RECIPROCAL INHIBITION IN SMALL NERVE NETS

The best direct evidence for the existence of
reciprocal inhibition networks in muscle control
systems appears to be the special neurons described by, and named after, Renshaw14 • The investigation of Eccles, Fatt, and Koketsu 5 expanded
the evidence that Renshaw cells are responsible
for rather widespread inhibition. They also suggest that Dale's principle to the effect that all
axon terminals of a given neuron must be of the
same kind (all inhibitory or all excitatory in our
model) and, therefore, that motor neurons, having
excitatory terminals (again we simplify the statement to suit our model), could not have inhibitory
terminals on each other. The Renshaw cells may
therefore be interposed to provide inhibitory terminals. The neurons bl and b2 would serve essentially the same function as Renshaw cells.(Fig.14).
However, Eccles et al make no mention of the
demonstrated or possible occurrence of a multivibrator effect. Unfortunately they, like Renshaw
and others, excite these spinal neurons (in cats)
only by brief antidromic volleys in the motor neurons, a procedure unlikely to bring forth multivibrator action.
Thus the empirical evidence is sketchy and only
suggestive.
Conclusion
Reciprocally inhibiting neurons must be able to
transform a relatively constant frequency stream
of impulses into rhythmic bursts of impulses if
our conceptual and derivative simulation models
are reasonably valid. The multivibrator effect
does not appear to be critically dependent on narrow ranges of parameter values. Minor differences
in the parameters of two hypothetical elements
facilitate rather than hinder the effect, which is
important in light of the probable fact that no
two real neurons are identical in behavior.
While the multivibrator-effect reliability
appears over a substantial range of parametric
conditions, it is not a rigid mode of behavior.
The dominance ratio, mean frequencies during dominance, and lower and upper limits of the mode are
all subject to regulation by signals. On the
other hand, random fluctuations of the input frequencies have little effect. Thus reciprocal inhibition provides a viable mechanism for producing
rhythmic behavior with varying degrees of automatic adjustment to prevailing enviror~ents.
On the basis of fragmentary empirical evidence,
fatigue was chosen to produce the necessary frequency decay in a dominant element. However, the
multivibrator effect might as well be produced by
adaptation at synaptic junctions. If the effect
occurs in real nerve nets, both adaptation and
fatigue probably play important roles.
The material presented here constitutes an exploratory study of reciprocal inhibition between
two elements only. Even this simple system requires and deserves more thorough investigation.

183

We are not certain that all of the major, much less
secondary, modes have been observed. The analog
and digital simulation models have proved to be invaluable tools. The main advantages of the digital
program have been the precise control and recording
of events, the ability to automatically carry out
sequential and simultaneous groups of experiments,
and the ease with which model changes can be made.
Its main disadvantages have been the necessity of
transcribing printed output into firing plots suitable for rapid visual scanning and the economic
necessity of restricting digital elements to coincidence firing. The analog's advantages were the
ease with which parameters could be altered while
observing the consequences directly, output in a
form that can be rapidly scanned, relaxation firing,
and small size. Its disadvantages were the difficulty of precisely controlling and observing the
parameters and artifacts and the inability to execute sequences of experiments automatically.
Acknowledgments
We are pleased to acknowledge the support of the
U. S. Air Force Office of Scientific Research,
Contract AF 49(638)-1021, in the investigations reported here. Special thanks are due Miss Alice
Opolak for her coding and operation of the digital
program and her patient testing of numerous parameter variations. Similarly, we are indebted to
Dr. E. D. Lewis for the design, construction, and
operation of the analog simulation models.

References
1.

Burns, B.D.: "The Mechanism of After-bursts
in Cerebral Cortex" J. Physiol (1955), Vol.
127, 168-188.

Burns, B.D.: "The Mammalian Cerebral Cortex"
London, 1958.

Brazier, M.A.B.: "The Electrical Activity of
the Nervous System" 2nd Ed. New York, 1960.

Creed, R.j Denny-Brown, Dj Eccles, J.C;
Liddell, E.G. j Sherrington, C.S.: "Reflex
Activity of the Spinal Cord" Oxford, 1932.

Eccles, J.C.; Fatt, P.i Koketsu, K.:
"Cholinergic and Inhibitory Synapses in a
Pathway from Motor-Axon Collaterals to Motoneurones" J. Physio!. (1954), Vo!. 126,
524-562.

Fessard, A.: "The Role of Neuronal Networks
in Sensory Communications within the Brain"
Sensory Communication (W.A. Rosenblith, Ed.)
New York, 1961.

Grani t, R:
Yale, 1955

Harmon, L.D.: "Artificial Neuron"
(1959), Vol. 129, 962-963.

''Receptors and Sensory Perception"
Science

DATA ANALYSIS AND MODEL CONSTRUCTION IN THE STUDY OF THE NERVOUS SYSTEM

184
9.

Harmon, L.D.; Wolfe, R.M.: "An Electronic
Model of a Nerve Cell"
Semiconductor Products, Aug. 1959, 36-40.

10.

11.

14.

Renshaw, B.: ''Influence of Discharge of
Motoneurons upon Excitation of Neighboring
Motoneurons" J. Neurophysio. (1941),
Vol. 4, 167-183
'

Hoyle, G.: Lecture: "Experimental Analysis
in the Intact Insect" California Institute
of Technology; Jan. 12, 1962.

15.

Josephson, R.K.; Reiss, R.F.; Worthy, R.M.:
"A Simulation Study of a Diffuse Conducting
System based on Coelenterate Nerve Nets"
J. Theoret. BioI. (1961), Vol. 1, 460-487.

Sherrington, C.S.: "The Integrative Action
of the Nervous System" Yale, 1906.

16.

Taylor, W.K.: "Electrical Simulation of
some Nervous System Functional Activities"
Third London Symposium on Info. Theory
(C. Cherry Ed.) London 1956.

17.

Taylor, W.K.: "Computers and the Nervous
System" Models and Analogues in Biology:
Symp. No. 14, Soc. Exp. BioI. New York, 1960.

12.

McDougall t W.: "The Nature of Inhibitory
Processes within the Nervous System" Brain
(1903), Vol. 26, Part 2, 153-191.

13.

Reiss~

R.F.: "The Digital Simulation of
Neuro-Muscular Organisms" Behavioral Science
(1960), Vol. 5, 343-358.

THEORY AND SIMULATION OF RHYTHMIC BEHAVIOR DUE TO RECIPROCAL INHIBITION IN SMALL NERVE NETS

Input

d e

.
f

I
I\

I\
I \
I

I
Q

........

-----

s
o

smIn
.

Output

Figure 1. Response of Sand

e to Excitatory and Inhibitory Impulses.

185

186

DATA ANALYSIS AND MODEL CONSTRUCTION IN THE STUDY OF THE NERVOUS SYSTEM

\-~--- 1\--~--~-"'
\
I
I

I's

,
I
I

Emax

Figure 2.

Inp ut

J.1U,C b .L

Fatigue Effects of Firing; Stimulant S Held Constant.

a.l.V~

Impulses

Inhibitory
Integrator ~

Stimulus
Sum

r-+

Monostable
Flip-Flop

Output
.Impulses

~ ~

Fatigue
L'"1tegrato.L

Figure 3. Major Components of Electronic Analog Neuron.

THEORY AND SIMULATION OF RHYTHMIC BEHAVIOR DUE TO RECIPROCAL INHIBITION IN SMALL NERVE NETS

Arrowheads == excitatory axon terminals)
inhibitory axon terminals
( Solid circles

Figure 4. Reciprocal inhibition network equivalent to that proposed in
1903 by MCDougall 12 to explain alternating reflexes.

187

DATA ANALYSIS AND MODEL CONSTRUCTION IN THE STUDY OF THE NERVOUS SYSTEM

188

Figure 5. Basic reciprocal inhibition network
with one input element (a l ).

IIIII1111111111111111111111111111111111111111111111111III

I II I

I II I I

Figure 6. Firing patterns of elements in network of Figure 5,
showing multivibrator effect with two types of switchover.

THEORY AND SIMULATION OF RHYTHMIC BEHAVIOR DUE TO RECIPROCAL INHIBITION IN SMALL NERVE NETS

-s::
00

"0
0

CD
00

100

• .-1

-t
-t
• .-1

S
.......
-t
~

>
~

1::

t-o-4

s::
~
s::
• .-1
S
0

50
40
30
J

I
300

350

400

450

500

Input Frequency (pulses per second)

Figure 7. Typical variation of dominance intervals in two reciprocally
inhibiting elements w·ith asymmetric parameters. (Digital Simulation).

189

I-'

2. 5

..........
00

'---1"P-'T-----r-----.-----

2.0

>
~
>
z
>
t:"'"

~~
()

00
........

>-<
c.n

.....cd

>
Z

r...

(1)

+.J
$:~

1.5

s:::

.....

t:"'"

t:%j

n
o

cd
$:~

zc.n

·M

..,g
o
:%

1.0

..,z
::c
t:%j

..,c.n
0.5

c:::

_ _ _ _ _ _ _ _ _ _ _ _ __L__

Input Frequency (pulses per second)
Figure 8. Variation of dominance intervals in two reciprocally inhibiting elements
with highly asyrrlmetric parameters. Illustrates linear and nonlinear
extremes of dominance interval behavior. (Analog Simulation).

100

'>-<
="

o'"I'l

..,
::c
t:%j
zt:%j
::0

c:::
c.n
c.n
>-<
c.n

..,

t:%j

s:::

THEORY AND SIMULATION OF RHYTHMIC BEHAVIOR DUE TO RECIPROCAL INHIBITION IN SMALL NERVE NETS

Figure 9. Basic reciprocal inhibition network
with two, independent input elements.

111111

III I

11111I1

1111

Figure 10. Multivibrator effect with overlapping switchovers.

191

192

DATA ANALYSIS AND MODEL CONSTRUCTION IN THE STUDY OF THE NERVOUS SYSTEM

Figure 11. Reciprocally inhibiting elements driving efferents d1 and d2 ,
with lateral inputs b 1 and b2 for control of dominance ratio.
Elements ml and m 2 represent antagonistic muscles.

THEORY AND SIMULATION OF RHYTHMIC BEHAVIOR DUE TO RECIPROCAL INHIBITION IN SMALL NERVE NETS

Figure 12. Reciprocal inhibition network with stretch receptors
regulating dominance ratio to match unequal loads on m 1 and m .
2

193

DATA ANALYSIS AND MODEL CONSTRUCTION IN THE STUDY OF THE NERVOUS SYSTEM

194

I I I I I I I I I I I I I I I I II I I II I
11111

11111

Figure 13. Semi-multivibrator mode due to
asymmetric parameters.

Figure 14. Reciprocal inhibition via intermediate elements
bland b 2 as suggested by the study of Renshaw cells (Eccles,
Fatt and Koketsu 5), and satisfying Dale's Principle.

195

THE MANIAC III ARITHMETIC SYSTEM
Robert L. Ashenhurst
Institute for Computer Research
University of Chicago
Chicago, Illinois
Summary

Code

Number

Unlike most computers, for which there is a
formal distinction between "fixed-point" and
"floating-point" numbers, the University of
Chicago Maniac III computer handles all numbers
in a single format (exponent and coefficient,
with the coefficient in general not normalized).
This permits several types of arithmetic to be
defined, which differ in that results are adjusted (coefficient scaled) according to different rules. These rules are classified in terms
of "significant-digit," "normalized," "specified
point" or "basic" characteristics. Since the
operand format in all cases is the same, numbers
can be processed by the various arithmetics without intermediate conversion, thus adding a dimension of flexibility to the computing process.

10 ..... 00

-1
_1+2- 39
_1+2- 38

This paper discusses the Maniac III arithmetic rules in some detail, showing how they
embody the cited characteristics, and how consistent conventions for rounding, adjustment of
zero and formation of low order parts are established. The trapping system used for the detection of anomalous results is also described.
1. Number Representation
Maniac III has a 48-bit word, which is partitioned for purposes of numerical manipulation
into an 8-bit exponent part and a 40-bit coefficient (fraction) part. The exponent bits~
numbered from right to left, and the coefficient
bits from left to right, starting from 0 in
either case. The format is diagrammed in Figure
1.
7 ••• 0

0 ........... 39

Figure 1. Numerical format
Any sequence f f ... f
of bits in the
39
Ol
coefficient section represents a number f in the
range -1 ~ f ~ +1_2-

, according to the formula

Lk=l
(see Table 1).

This is the familiar scheme in

10 ..... 01
10 ..... 10

l1..~

.. ll

-2

00 ..... 00

-39

0
+2- 39

00 ..... 01

01. .... 10
01. .... 11
Table 1. Coefficient coding
which non-negative numbers are represented in
standard binary form (with implicit binary point
between fO and f ), while negative numbers are
l
represented in the corresponding (true or two's)
complement form. The bit fO is called the sign
bit of the representation; fO
and fO

1 when f < O.

when f

If f is negative, the

sequence of bits to the right of fO represents
(in standard binary form) the positive number
f* satisfying f*+lfl = 1, so that f = -l+f*.
From this it is easily seen that, as indicated
by the table, every positive number f which can
be represented has a negative -f which can also
be represented, and the only negative number for
which the reverse does not hold is f = -1.
For f > 0, the number m ~ a of leading
digits of f is defined as the number of consecutive bits 0 appearing to the right of the binary
point in the representation of f. Evidently
m = 0 when 1/2 ~ f < 1, m = 1 when 1/4 " f < 1/2,
and so forth. When f = 0, m = 39 by convention,
and for -1 < f < 0, m is defined to be the number of leading digits in the positive number -f.
For all negative f f _2- k , this is just the number of ~onsecutive bits 1 appearing to the right
of the binary point in the representation of f;
-k

if f = -2 ,m is one less than this number.
f = -1, m is undefined.
Any sequence e e ... e of bits in the
O
7 6
exponent section, except the sequence 00 ... 0,

196

COMPUTER SYSTEMS

represents an integer e in the range -127
+127, according to the formula

+L
k=O
(see Table 2).

This is an "excess-128" scheme, in
Code

Number

00 •.• 01

-127

00 ... 10

-126

01. .. 11

-1

10 ... 00

10 ... 01

I
11. .. 10

+126

11. .. 11

+127

Table 2. Exponent coding
which each exponent e is represented by the
sequence of bits which would represent e + 128 in
standard binary form. The bit e is called the
7
exponent sign; e = 1 signifies e ~ 0, while
7
e s 0 signifies e < O. For each possible posi7
tive exponent e there is a corresponding negative,
and vice-versa, without exception. The sequence
00 ... 0, however, is not assigned a numerical
value; it is denoted e and called the exponent
Z
for "absolute zero," as explained subsequently.
If e ; e ' then the pair f,e is taken to
Z
to represent a number x,

If f1

= fO'

then the same number x is ob-

tained by shifting the coefficient pattern one
place left (i.e., replacing fk with f + for
k l
k = 0,1, ..• ,38, and f39 with 0), and subtracting
1 from the exponent, since

= x,
and the left shift effectively doubles the coefficient. If f ; 0) this process can be repeated
until fl ; fO' in which case the number x is said
to be in normalized form. In general, m = 0 for
a normalized form; the only exception occurs when
x = _2- k for some k > 0, in which case f = -1 in
the normalized form and m is undefined. For
f = 0, the normalized form itself is undefined;

the number x = 0 is represented by f = 0 with any
numerical exponent e whatever. The number x = 0
is also denoted by e = e and any coefficient f
Z
whatever; this version of 0 is termed absolute
~; and is subject to different arithmetic rules
than the versions with coefficient 0 and e FeZ'
any of which is termed relative zero.
The foregoing discussion shows that number
representation in the coefficient-exponent system
is, in general, not unique. It has been customary
to take the normalized representation as standard,
with special rules to cover the case of zero coefficient. Thus "floating point" arithmetic units
are conventionally designed to handle operands in
normalized form, and to generate normalized results. In Maniac III, by contrast, the arithmetic
unit handles unnormalized as well as normalized
operands in a meaningful way, and generates results whose form depends not only on the form of
the operands, but on which of several types of
arithmetic is called for: Floating Point, Specified Point, Normalized, or Basic. Floating Point
results are adjusted according to a "significant
digit" criterion; Normalized results are adjusted
to normalized form. Specified Point and Basic
arithmetic both generate results whose form depends on the operand exponents. More detailed
descriptions of the different types of arithmetic
are given in subsequent sections. It should be
noted here, however, that Maniac III has no
"fixed point" arithmetic which operates on numbers in pure coefficient form, as do conventional
computers. Hence the usual distinction between
"fixed point" and IIfloating point" numbers need
not be made in numerical work, and no formal conversion is necessary to employ the result of one
type of arithmetic operation as operand for
another.
2. Numerical Results
The Maniac III operations which are relevant to the discussion comprising this and the
following three sections are: Add, Multiply,
Divide (Floating Point); Add, Multiply, Divide
(Specified Point); Normalized Add, Square Root,
Sign, Adjust, Scale.* All Add, Multiply and
Divide operations can be performed with a sign
option for the second operand; hence subtraction
is included as a case of addition. Coefficient
scaling (shifting), with or without corresponding
exponent alteration, is performed by means of the
Adjust and Scale operations, while the Sign operation is a conditional negation, from which negatives and absolute values can be obtained as
special cases.
In this section some general considerations
regarding numerical results are discussed; this
serves to provide a context in which detailed
features of the individual operations may be
better understood.
*This does not include Basic arithmetic,
which is discussed in Section 6.

197

THE MANIAC III ARITHMETIC SYSTEM

Normally, two words are used to express the
complete result of an arithmetic or numerical operation in Maniac III. These are developed in two
central registers designated U (for Uniyersal) and
R (for Residual); the contents of these registers
are denoted u and r, respectively. In some operations the result u,r is to be interpreted as u + r
(with r a low order part, small in magnitude compared to u), in others as u with remainder r. In
some operations the R register is not used at all,
in which case u alone represents the result in its
entirety. In any case, u is the approximate result generally used in further computation.
For each of the operations under consideration there is defined a IItrue ll (arithmetically
exact) result, expressible as a single number in
the case of Add, Multiply, Adjust, Scale and Sign,
or as two numbers, one of which is a remainder, in
the case of Divide and Square Root. Furthermore,
these numbers are all representable with a finite
number of binary digits, and their adjustment
(binary point positioning as expressed by the
exponent) is uniquely determined. Sometimes,
however, this "true" result is not produced by
the computer. The reasons for this may be categorized as follows:
(a)

(b)

(c)

The exponent of result or remainder
is out of the representable range
-127 ~ e ~ +127;
The coefficient of the result is out
of the representable range
-39
-1 ~ f ~ +1-2
;
The coefficient of the result or
remainder is truncated so that some
of its rightmost digits do not appear.

The three effects are, of course, not unrelated;
in fact, a case of (a) where e < -127, if it
arises during the course of an operation, is
generally converted to a case of (c) by successively halving the coefficient (by right-scaling,
so that low order digits are lost), and incrementing the exponent until it reaches the value
-127.
During the running of a program, if a final
result is generated in which either (a) or (b)
obtains, a trap condition is initiated which
causes a program interrupt (unscheduled jump),
unless specifically overridden by instructions
available for the purpose. In case of (c),
however, no special computer action is invoked,
since the numerical error committed, unlike that
of the other two cases, is small. In all three
situations, however, the result actually developed
by the computer can be interpreted in terms of the
"truel! one; in (a), all digits of the exponent
except the sign are correct, in (b) and (c) the
coefficient sign is the actual one, and all other
digits are those which would appear in the corresponding part of the coefficient if it were to be
developed in full.

A trap condition also occurs in special
cases where no "true" result is defined (e.g.,
because of zero divisor, square root operand
negative or scaling parameter out of range). In
some such situations a partial or related result
is generated, depending on the nature of the
anomaly.
In order to discuss the operations in
detail, it is convenient to extend the nomenE
F
clature as follows: U and U are the exponent
and coefficient sections, respectively, of U; uE
..
f sequences uEE
an d u F , cons~st~ng
0
u ... u E an d
O
7 6

u~u~ ... u;9' respectively, denote the corresponding contents. Similar conventions apply to R and
any other registers which may be introduced. In
an operation whose result is defined as u + r,
the non-sign coefficient positions of R generally
contain the low-order continuation of the coefficient residing in U; that is, the coefficient of
the result is represented by the 79-bit sequence
F F
F F
F
uOul ... u39rl ... r39' The u + r interpretation is
consistent with this if rE

u -39 and rO

= O.

This rule for the exponent is the one actually
used, unless rE < -127; in this case, r is adjusted to exponent rE = -127 as explained earlier. The u + r interpretation then still holds
(although rF may have lost some non-zero digits
at the r~ght), but the 79-bit interpretation must
be modified.
The 79-bit interpretation is also affected
F

when rO

= 1,

which occurs frequently because of

the method of rounding employed in the Ma~iac III
system. Rounding is defined as follows: Consider a coefficient sequence fOfl ... f of arbin
trary length n, and suppose it is desired to
replace this with a shorter sequence whose last
bit is in place p. The rounded sequence is taken
as fOfl ... f p if (i) fp = 1 or (ii) fP+l = ...

= f n = 0;

if f

= 0,

however, and condition (ii)

is not met, the rounded sequence is taken as
fOfl ... fp_ll. Thus the last bit of the rounded
sequence is always 1 unless truncation involves
no approximation (i.e., only bits 0 are dropped~*
*This rounding scheme has twice the spread
("variance") of the more conventional one where
F
u is altered by addition of 1 in the pth place
if the part dropped exceeds 1 in the (P+l)st
place; however, the scheme described here also
has some advantages, both theoretical and practical, over the traditional one. First, it is symmetric (llunbiased"); the mean of the numbers
F
which round to a particular value u is uFo Second, it is non-propagative; only the rightmost
F
digit of the number u is altered in rounding,

COMPUTER SYSTEMS

198

It should be noted that under these rules the operations of rounding and negation commute; i.e.,
the negative of a rounded value is the rounded
value of the corresponding negative.

considered to be met if and only if u ~ x, where
x is a number in memory. If u is absolute zero
while x is relative zero, the condition is considered not to be met, since by the above definition u < x under these circumstances.

In practice, a rounded result u is computed
from a full result u + r by "forcing l ' u;9 to 1 if
any digits 1 have been "shifted off" into the loworder region. If u F = 0 originally, this amounts
39

Some of the convenient features of the
Maniac III system which can be appreciated even
from this preliminary discussion are:
(a)

the adjustment for e < -127 means
that small numbers never get converted into large ones through
exponent underflow, which makes
it unnecessary to avoid the low
end of the numerical scale;

(b)

the non-exceptional nature of
relative zero for the system,
and the consistency of the interpretation of absolute zero, per.mit
results involving zero to be much
more naturally defined;

(c)

the rounding scheme, in addition
to its theoretical advantages,
gives rise to results which are
simultaneously rounded and correct
as two-word representations, thereby
making it unnecessary to have an
option for rounded arithmetic;

(d)

in the majority of cases results
have a consistent interpretation,
even where they are anomalous,
which simplifies the general task
of the analysis and control of
sequences of arithmetic operations.

u -39, this increF

mentation can be compensated for by setting rO to
E

u
1, thereby subtracting 2 -39 from r and leaving
the u + r interpretation valid. This step is
always taken before any necessary adjustment of r
for rE < -127; thus it can be said that the u + r
interpretation always holds, to a suitableappraximation, given only that the exponent and coefficient of u have themselves stayed within range.
When r is a remainder instead of a loworder part, the interpretation is always arithmetically exact (i.e., in division, dividend =
quotient x divisor + remainder, etc.), unless
rE < -127 necessitates adjustment of r. In the
case of division, a rounded quotient u is obtained, and the remainder r compensated accordingly; in the square root case, however, no
rounding takes place, and the remainder is always
positive.
Because there is no normalized standard
form, zero results may be expected to occur more
often in this arithmetic system. Cases where one
or both of u and r are relative zero as the result
of the operation arise naturally, and are subject
to no conventions additional to those described
above. Absolute zero (exponent e ) can occur as
Z
a result only if one or possibly both operands
are absolute zero (specifically, both operands
in addition, one or both operands in multiplication, one operand (dividend) in division, and
the single operand in the adjust, scale, sign and
square root operations).

In these cases, both u
F
an d r E are set to e ' an d both u and rF to 0 .
Z

One further property of absolute zero should
perhaps be mentioned here. In the natural ordering of computer numbers, absolute zero is
taken as greater than any number with negative
sign and less than any number with positive sign;
the latter category includes relative zero. The
effect of this convention is only apparent in the
result of the (quasi-arithmetic) instructions
Jump on Arithmetic Comparison and Jump on Magnitude Comparison, in which a jump condition is
and this both simplifies the mechanization and
would seem to be advantageous in situations where
rounding error does not behave like a symmetric
random variable.

3. Fundamental Arithmetic Operations
The operations Add, Multiply and Divide
each require two operands; one of these is taken
from register U, the other from memory. The operand from memory is first fetched to a register
designated S (for Storage), The procedure then
implemented can be symbolized by
u

(is) -

u,r

where * is either +, . or /, and the +,- alternative is specified in the instruction calling
for the operation.
The operations designated Floating Point
are defined in terms of the adjustment of
their results, as follows: for Add, the result
appears adjusted to the larger of the two operand
exponents, while for Multiply and Divide, the
result appears adjusted so that its number of
leading digits m is given by m = max(m ,m ),
l 2
where m ,m are the corresponding numbers associl 2
ated with the operands.
If the value of each operand is regarded as
uncertain in the 39th place, then the transmitted

199

THE MANIAC III ARITHMETIC SYSTEM

uncertainty in the result, adjusted according to
these rules, will also be approximately in the
39th place; hence the informal characterization
"significant-digit arithmetic." These adjustment
rules are more than mere ru1es-of-thumb, however;
they have desirable characteristics with regard
to the propagation of errors of arbitrary magnitude, and their formal consistency also recommends
them (see Reference 1).
Exception is made to the rules as described
when adjustment is necessary to keep the coefficient within range, or to avoid the exponent conE
dition u < -127; the required adjustment in both
cases involves a right-scaling of coefficient,
which is in the direction of decreasing apparent

significance. Adjustment for u > +127 requires
a left-scaling of coefficient; even if this would
not take the coefficient out of range, it would
increase its apparent significance, and so the
step is not undertaken. The case therefore
causes a trap condition.
Relative zero operands in multiplication
and division are handled in a way consistent
with the interpretation m = 39; the result is
always zero with an appropriate exponent (even in
the case of relative zero divisor, which is a
trap condition). Absolute zero operands, however,
act like the true zero of the number system,
obeying the rules
x + 0

x·O

O·x = 0;

O/x

= 0;

+ x

The third type of arithmetic to be discussed is Specified Point, which supplants the
conventional "fixed-point" operation. Here Add,
Multiply and Divide are all three subject to the
same type of rule: the result is adjusted so
that its exponent is equal to the exponent of the
first operand (that originally residing in U).
The only exceptions occur when absolute zero operands are involved, in which case the behavior
is the same as for the floating point operations.
Following the specified point rules obviously never leads to out-of-range exponents, but
the required adjustment may cause the coefficient
to exceed its permitted magnitude. When this
happens the sign and remaining bits which do
appear are correct (i.e., are part of the true
resul~) as mentioned earlier; since high order
digits have been lost, however, a trap condition
obtains.

4. Further Numerical Operations
The operations Square Root, Sign, Adjust
and Scale are not explicitly characterized as to
arithmetic type, but their definitions reflect
the general arithmetic philosophy outlined above.
Square Root is performed on an operand
fetched from memory to S, according to the
formula

= x;

x/O undefined (trap,
no operation).

When absolute zero is produced as a result, it is
always with coefficient 0, regardless of the coefficients attached to the absolute zero operands
involved.
The multiplication and division operations
described above have the property that if they
are performed on normalized (non-zero) operands,
the results are produced in normalized form also.
(An exception, of generally trivial consequence,
arises for a result which is exactly a negative
power of 2, since the m = 0 form is not normalized
in this case.) Hence only one further operation,
Normalized Add, is needed to permit calculation
to be carried out fully normalized in standard
fashion. Normalized Add gives a normalized,
rounded result regardless of the original adjustment of the operands. The only exceptions occur
when continued adjustment by left-scaling fails
E
to normalize the coefficient before u = -127 is
reached (this includes the case of relative zero
result). Such an unnormalizab1e result always
gives rise to a trap condition, which permits
contingent procedures to be defined by program.
However, an absolute zero result, which can only
occur through addition of two absolute zero operands, does not lead to a trap condition.

±F-u,r.
The result in U has the same number of leading
digits as the radicand, and is not rounded; this
allows the remainder in R to be treated as meaningful (i.e., (square root)2 + remainder = radicand). Square Root thus has the character of a
floating point operation. If the operand is
absolute zero, both the result and the remainder
are absolute zero with coefficient O. If the
operand is negative, a trap condition occurs; in
this case, however, a square root is still computed, that of the operand negated.
The Sign operation is defined as follows:
an operand is fetched from memory to S, following which one of two alternatives is effected;
either

±s-u
if u

0 originally, or
+s-u

if u < 0 originally. The +, - alternative is
specified in the instruction, as usual. If the
operand is absolute zero, then the result is absolute zero with coefficient O. One use of this
"conditional negation" is to form absolute
values; if the operand is taken as u itself (possible because U has a memory address in Maniac
III), then the + alternative effectively performs

200

COMPUTER SYSTEMS

categories, as follows:

lul---u,

(1)

Coefficient Trap--the coefficient has
gone out of range, and digits have been
lost at the left (specified point type
operations).

(2)

Exponent Trap--the exponent has gone
out of range, causing its sign to
change spuriously (floating point type
operations, range exceeded positively).

(3)

Parameter Trap--the scaling parameter
n has been specified outside the range
-128 ~ n ~ +127 (on Adjust and Scale).

(4)

Operation Trap~=the operation has not
been completed according to its definition (divisor is zero, or radicand is
negative; result is unnormalizable, or

while the - alternative performs

-Iul-u.
The contents of R are undisturbed by this operation. The result normally takes the exponent of
the operand; adjustment is made, however, for outof-range coefficient (which can only occur on
negation of -1). The Sign operation may therefore
be classified as floating point.
The Adjust and Scale operations are two
versions of "arithmetic shift." They both basically involve a single operand and a parameter n
in the range -128 ~ n ~ +127. In Adjust, the operand is fetched from memory to S, transmitted
(positively or negatively) to U, and then adjusted
_

_ __

_ _

by adding n to u- and scaling u- (With r-) accordingly. Thus, if n > 0 the coefficient is scaled
to the right, (successive halving), and if n < 0
it is scaled to the left (successive doubling).
The numerical value of the number u is unchanged,
except insofar as digits are "shifted off." The
full result is u + r, with u rounded in the usual
fashion. If the operand is absolute zero, then
the final values of both u and r are absolute
zero, with coefficient O.

adjustment cannot be

These are collectively referred to as arithmetic
traps, to distinguish them from other kinds of
trap conditions which can occur in the course of
computer operation (namely, instruction traps and
real time traps). There is a fifth category of
arithmetic trap, reflecting a feature of the
Maniac III register structure which has not yet
been mentioned: Each of the registers U, R and
S has one extra digit position, designated

Exceptions occur when the performance of
the operation as defined would force the exponent
or the coefficient out of range. In these cases
the floating point conventions are followed; the
operation is carried to completion in the face of
E
u > +127, but suspended otherwise; either case
gives rise to a trap condition.
Scale is similar to Adjust except that the
exponent is not altered; thus the operand is effectively multiplied by a power of 2,
2

-n

(.±u) -

u, r.

The scaling process is carried out completely,
even if this causes loss of high-order digits at
the left. Thus Scale resembles a specified point
operation, in contrast to Adjust.
The parameter n is defined in a computer
instruction as a l4-bit integer; however, unless
the leftmost 7 bits are identical (i.e., unless
-128 ~ n ~ +127), no operation is performed and a
trap condition results.
With n = 0 and the - alternative, either
Adjust or Scale acts as a negation operation;
they differ in that the former keeps the coefficient -1 in range by right-adjustment, while the
latter does not.
5. Trap Conditions
The trap conditions mentioned in the foregoing discussion are classified into four

~ and

si,

ui,

respectively, which may be considered

to lie immediately to the left of the sign position (coefficient position 0). This means that
the actual range of coefficients these registers
.
-39
can hold is -2 ~ f ~ +2-2
. In the operations
discussed thus far, these extra positions are
used for internal convenience only, and a result
with ui ; u~ (which is the condition for u outside
-39
the normal range -1 ~ u ~ +1-2
) can never be
generated. The Basic arithmetic operations discussed in the ne."Ct section, however, can leave U

in the condition ui;

u~, and it is to protect

against the initiation of a non-Basic operation
under these circumstances that the fifth trap condition is introduced:
(5)

Segment Trap--the condition

x ; Uo

obtains at the start of a non-Basic
operation which uses u as an operand.
Each arithmetic trap condition, when it
occurs, causes a corresponding trap toggle (l-bit
register) to be set to 1. At the completion of
the performance of the instruction which gave
rise to the trap condition, the following instruction in sequence is fetched and examined by the
computer control. If this one of five special
Disable instructions, the corresponding trap
toggle is reset to 0, and the next inst~Jction is
fetched in turn. This allows the effect of any
anticipated arithmetic trap condition to be

201

THE MANIAC III ARITHMETIC SYSTEM

nullified by the computer program.
If any trap toggles are still set when a
non-disable instruction is finally encountered,
that instruction is not performed, but instead
the instruction residing in a special trap location is fetched and executed. At this time the
~ining trap toggles are all reset to O. However, the presence of each trap condition, whether
nullified or not, is recorded in a corresponding
trap indicator (I-bit register), by setting it to
1 if it is not already in that state; this occurs
immediately following the original arithmetic instruction, before any Disable instructions have
been acted upon.
The instruction in the trap location may be
a Jump instruction, specifying a new control address, in which case the trapping has effectively
caused the insertion of a special routine into the
program sequence. This routine may use the information recorded in the trap indicators to initiate
remedial procedures.
If the instruction in the trap location is
not a Jump, control reverts back to the original
point (i.e., to the instruction about to be performed before the interpolation of the special
instruction) after its execution. The trap indicators remain set in whatever configuration they
may have achieved, and so are available for use in
the main program.
This description of the essential features
of arithmetic trapping has ignored complications
which arise due to the possible simultaneous occurrence of trap conditions of the other types
(i.e., instruction and real time). A full development of these complications is irrelevant to
the purposes of the present discussion.
6. Basic Arithmetic
Still another category of arithmetic operation is to be included in the Maniac III repertoire. Basic operations are so called because
they employ exponent conventions which are in
some sense "natural"--in particular, the exponent
of a product is the sum of the exponents of the
factors, and the exponent of a quotient is the
difference of the exponents of dividend and divisor. However, these operations differ fundamentally from those discussed earlier in that they
may involve two-word operands, and that results
are defined in terms of the extended register
structure (X position included). The operations
are intended specifically to expedite the performance of multi-precise arithmetic, although
they are useful in other contexts also.
Multi-precise operands are assumed to be
defined by a sequence of 39-bit segments, possibly signed (as e.g. are produced by floating
and specified point operations). It is anticipated that either of two exponent conventions
might be appropriate: each segment might carry
the exponent of the entire number, or this

exponent might appear only on the highest order
segment, with the exponents on lower order segments decreasing by 39 at each stage (results of
ordinary arithmetic operations obey the latter
convention).
The category of Basic operations may be
considered to include Basic Add, Basic Multiply,
Basic Divide, and an additional operation designated Round to Nearest Value. The properties of·
these operations will only be sketched here. In
each case, one word is fetched from memory, and
this is combined with the contents of U and possibly R in a prescribed way to produce a doubleprecise result, one word of which is then stored
in memory.
In Basic Add, the result is a double-precise
sum, the high order part of which is retained in
U while the low order part is stored in memory.
The effect is to add the memory operand to the
operand initially residing in R and produce a sum
adjusted to the larger of the two operand elPonets (possible overflow being taken care of by
the extended register structure); to this sum is
added the number originally in uF , scaled as if it
carried an exponent 39 less than that of the
intermediate sum. Two multi-precise numbers can
be added by a succession of such operations; the
F

final contents of U at each stage are carried
over and applied to the addition of the next
higher pair of segments. (The exponents of the
two operands must not differ by more than 39 for
this procedure to be successful.) If the operand
exponents are identical, no scaling of segment
coefficients need take place; under these circumstances, the carry from each segment addition is
recorded in U~, and

records the sign of the

sum. The instruction Basic Add includes the
usual +,- option, so that it serves for subtraction, and it also has an option for initially
clearing U, to be used in cases where no lower
order segment is defined.
In Basic Multiply, the product of the operand initially residing in R and the operand
from memory is formed, with exponent equal to the
sum of the exponents of the factors; to this
product is added the number originally in uF ,
scaled as if it carried an exponent 39 less than
that of the product. The product of a singleprecise multiplicand and a multi-precise multiplier can be formed by a succession of such
operations, the high order segment of the product
at each stage being the increment added to the
low order product at the next stage. In combination with addition this procedure can be used to
form products of two multi-precise factors. The
instruction Basic Multiply includes a +,- option
for the multiplier and an option for initially
clearing U.
In Basic Divide, the operand initially
residing in R serves as divisor, and the dividend
is a two-word operand with the contents of U as

COMPUTER SYSTEMS

202

high order part and the number from memory as low
order part. Before the start of the division
proper, however, the contents of R are normalized;
the exponent of the quotient is then the difference between the exponent of the dividend and the
exponent of the normalized divisor. The quotient
of a multi-precise dividend and a single-precise
divisor can be formed by a succession of such
operations, the remainder at each stage being
used as the high order part of the dividend at
the next stage. To form quotients with the divisor also multi-precise, the division operation is
used to generate quotient digits, but multi-precise remainders are computed by multiplying and
subtracting (remainder = dividend - quotient x
divisor). To simplify the implementation of this
procedure, the instruction for Basic Divide has
a +,- option which applies to the remainder, as
well as the standard one for the divisor.
The Round to Nearest Value instruction combines a high order segment initially residing in
U with a low order segment fetched from memory and
introduced into R. If the low order segment is in
the range -1/2 ~ f < 1/2, the high order segment
39
is left unchanged; otherwise 2is added to or
subtracted from the high order segment, as appropriate, and the sign of the low order segment in
R is reversed. This may be regarded as effecting
a "traditional" rounding operation on the number
in U; in addition to its normal uses, such an
operation turns out to be useful in the performance of multi-precise division (applied to the
normalized divisor initially, it insures that the
quotient segments will be in range).
The definition of the Jump on Arithmetic
Comparison and Jump on Magnitude Comparison instructions mentioned in section 2 are framed in
terms of the extended register structure, thereby
permitting the result of a basic operation (in U)
to be arithmetically compared with a number from
memory (which, however, is necessarily in the
normal range).

increment at ion or decrementation of exponents by
1 are both processes which can be carried out
independently and concurrently in these registers
when no transmission among them is called for.
Finally, both the coefficient and exponent sections of all three registers have an extra stage
(for coefficients, it is the X position already
mentioned), which in many cases allows operations
leading to out-of-range numbers to be completed,
and the necessary corrections or invocation of
trap conditions to be made subsequently.
Supplementing the advantages offered by
these structural features, considerable effort
has been put into organizing the arithmetic procedures into a pattern of uniformity, to permit
their more efficient execution. Thus, for example, the three non-Basic Add operations (Floating
Point, Specified Point and Normalized) are all
realized by a single micro-program in the computer
control, in which the variations between arith=

metic types are taken into account by making the
performance of certain steps conditional. A
similar remark holds for the non-Basic Multiply
and Divide operations. For all non-Basic arithmetic, a single pattern of end-connections
between registers U and R suffices; so, for
example, whenever a call is made for both these
registers to be shifted right, a connection is
F
F
automatically set up to-effect u39~ r O' and to
conditionally effect 1 -

rF i f and only i f
X

= 1. The latter step is for the purpose of
39
recording whether or not any digits 1 have been
shifted out of U into R, which is the condition

for forcing u;9to the value 1 at the end of an
Add or Multiply operation (for rounding).
No attempt will
of the procedures for
The interested reader
involved set forth in

be made here to give details
realizing the operations.
may find some of the notions
Reference 2.

7. Computer Implementation
The implementation of the rather elaborate
arithmetic system described is facilitated by
several basic structural features of the Maniac
III computer. Transmission between any pair of
the central registers U, R and S is efficiently
realized by means of a universal communication
bus called the "central distributor," and this
bus is partitioned so that the exponent and
coefficient sections can be transmitted separately. Scaling of coefficients and/or

References
1. Ashenhurst, R. L., and N. Metropolis, "Unnor-

malized floating point arithmetic,"
Journ. ACM, vol. 6, no. 3 (July 1959)
pp. 415=28.
2. Metropolis, N., and R. L. Ashenhurst, "Signi-

ficant digit computer arithmetic," IRE
Trans., vol. EC-7, no. 4 (Dec. 1958---)-pp. 265-7.

203

AN ORGANIZATION OF AN ASSOCIATIVE CRYOGENIC COMPUTER
Robert F. Rosin
Information Systems Laboratory
University of Michigan
Ann Arbor, Michigan

Prepared under Contract AF 33(657)-7391. Part of the
work reported \'TaS performed by IBM at the Thomas J.
Watson Research Center, Yorktown Heights, New York,
in cooperation with the Bureau of Ships under Contract
Number 77508 (Project Lightning).
Summary
The design of a total computing system built
in the cryogenic medium and with an associative
memory is discussed. Topics include instruction
sequencing, addressing, indexing, input-output,
multi-programming and system programming considerations. The iterative nature of the design of
this computer, removing the necessity for much
special-purpose hardware, increases its reliability. The associative memory makes it a very
flexible and powerful computer.
Introduction
There exist in the literature several
articles describing various aspects of computers
equipped with cryogenic circuitry and associative
memories. It is the purpose of this paper to
assemble many of these ideas and several others
into a coherent study of the total system organization of an associative cryogenic computer. The
ideas are not sufficiently refined to constitute
a complete plan for a machine but they do reveal
some of the problems and opportunities which
would arise in such a project.
The motivation behind this discussion of
the organization of an associative cryogenic
computer lies in two considerations. Due to the
ease of designing relatively simple associative
memory cells in the cryogenic medium, the latter
appears to be one of the most economical media in
which to consider building an associative computer.
Correspondingly, as will be discussed more fully
later, it is advantageous to build cryogenic
computers of uniform logical blocks avoiding
special circuitry if at all possible.

m,_~

.Lll.Lb

..!_

.Lb

due to the difficulties which will exist in the
maintenance of a computer in a cryogenic medium.
The design of an associative machine meets this
criterion adequately. Thus, the justification
of the topic of this paper.
Cryogenics has forced us to reconsider what
we currently feel are normal machine functions
and control relationships. Primarily, a computer
built entirely of cryotrons would exhibit similar
cycle times in the storage unit, the arithmeticlogical unit and the control unit. In most
contemporary machines, functions such as indexing
and operations on special registers take place in
a length of time relatively much shorter than

memory access and rewrite. Indirect
addressing is relatively rapid compared to add
time in a contemporary computer. In a cryogenic
computer, especially one equipped with associative
memory, this is no longer true to the same degree.
While retrieval and store times will be slower
than most control functions (due to long line
length and the accompanying relatively slow
switching time) the relative difference will be
much less than that which we are used to considering.
The concept of an associative store also
implies some new thoughts with respect to
classical organization. l ,2,3,4,5 What we shall
call an associative memory has been defined as
"memory from which a word of data is retrieved on
the basis of part or all of the data contents of
the word. II Thus, in what may be called a fully
associative machine, there is no address decoder
per se since words are not identified by numeric
addresses but by their contents. It is customary
to denote part of the contents as the "tag" or
name of the word, and the remainder as the
contents or value. For example, a 48-bit word
might be broken into two 6-bit characters of tag
and a 36-bit value. When retrieving a word from
the store it is important that the portion of the
word not to be used in comparison with the
criterion be ignored or masked during the retrieval.
While it is not the purpose of this paper
to review previous work in cryogenic memory
circuits, a few new concepts should be discussed.
Figure 1 shows two sets of memory cells; those of
the persistent current loop variety (shown on the
~ight.~n,t~e 7~g~e) have b::n pr~:ious~~7.8.q
u.eocrluea III c;nelr many conIlgura"tlons. ,., "
The chain bit, shown on the left, was recently
disclosed by Seeber.2 We shall further modify
this cell for our own purposes. In principle,
this is a two-state device, the present state
denoted by that branch which contains current.
The source of current is at the upper left end or
zero state side of the chain. A resistive (nonsuperconducting) cross branch anywhere in the
chain will force current into the righthand
branch from that cellon down; hence these cells
are considered to be in the state 1. For
consistency, the cross branch will also be considered state l .
Figure 2 shows an association cell con-

COMPUTER SYSTEMS

204

structed from a chain bit. Notice that "read"
current will pass through the cell only if there
is current in the cross branch. Note also that
this case can arise only when this cell is the
uppermost with association current passing
through. Thus this bit position in memory selects
the first of the words positively associated with
the criterion to be matched.
A more complicated cell is shown in figure 3.
This is the sequence chain bit. It allows
sequencing of the zero side down one word upon
reading of the cell if desired. This type of
bit, also called a "marker" bit, is central to
our discussion and will appear in several places
throughout this paper.
The criteria which have guided the specification of this machine (and might be applied to
the design of any other machine) are the
following:
1) it should be able to execute a well\·rritten program efficiently j
2) it should be able to translate a program
written in some higher level language into its
own machine language effiCiently,
3) it should be able to carry out inputoutput operations effiCiently, and
4) it should be able to interrupt normal
program control to handle exception conditions.
The nature of associative storage has influenced the application of these criteria.
The Computer
It is appropriate to begin the description
of the associative cryogenic machine with the
internal word formats, of which there are two:
data words and instruction words. (Fig. 4) In
this regard, it should be noted that serious
design criteria helped determine these formats,
but they are open for appraisal and change.
Data words consist of 25 control bits (an
arbitrary figure which should be adjusted to fit
the final machine design), a 48-bit tag field
(six 8-bit characters), and 64 bits of data along
with 3 associated flag bits, giving a total of
140 bits. The function of the control bits will
be described as the paper proceeds. The instruction word format consists of the same 25
control bits, a 48-bit address part, 2 bits for
addressing mode (indirect and immediate), a 15bit operation code, a 48-bit index address and
its 2 associated addressing-mode bits. Each
format should carry its appropriate checking
information appended to the right-hand end of
the word. It will be noted in the figure
that the tag field of the data word and tne
address part of the instruction word occupy the
same field of the basic word.
The nature of this machine's design in
conjunction with the operational characteristics
of chain bits places one restriction on the
location of data and instructions in the store.
They may be mixed to arcy degree desired; blocks
do not have to be contiguous, but all blocks of
data and instructions must occupy sequentially

ordered locations in the store. For example,
instructions, which appear in a block and are to
be executed in a linear sequence, must a-ppear in
the order in which they are to be executed,
although data words may appear interspersed anywhere in the instruction array. The same rule
applies to blocks of data where indexing is to be
used for individual word retrieval.
Instruction Seguencing
The six-character tag field seems adequate
for all data and storage names. It should be
noted that longer names requjre more bit positions
in every word in storage. Examination of the
formats presented above shows us that instruction
words do not have space for their mm tags, that
is they have no names. In the average large
scientific program, of let us say 32,000 words,
about 80% are data and the rest instructions. Of
the instructjons in the program at most 1/4 are
referred to by name. This amounts to, at most,
1600 words. If we were to lengthen the machine
word by 48 bits to accommodate a tag part for
each instruction, we would be adding over 1.5
million bits to our 32,000 word machine. If, on
the other hand, we stipulate that every instruction which we wish to refer to has a data word
between it and the previous instruction and that
this data word has a unique tag, then as will be
shown, control can be transferred to this tag.
Let us discuss instruction sequencing and
introduce two of the control bits. They will be
called the instruction bit (called the IB and of
the persistent current loop type) and the
instruction-used bit (called the IDB and of the
sequence chain type). Each word in storage which
is an instruction will have its IB set to 1, all
other words will have their IB set to zero. This
will be the duty of the translators and loaders
used with this machine. The TUB's of all words
above the next instruction to be executed will be
set to O. The TUB's of all words, including the
next instruction to be executed and below, will
be set to 1. To retrieve the succeeding instruction, the machine retrieves a pattern of 1, 1 for
the IB and IUB respectively. The other bits are
ignored (masked out) for the retrieval. (Masking
will be discussed later.)
The first word
from the top in storage which.has this combination of IB and TUB is the instruction sought, and
will be the only one positively associated. This
instruction will be read into the decoder to be
executed and the IDB's for all words down to and
including this word are set to O. This is we~
and good for normal processing, but what about
transfers both forward and backward in storage,
especially when instructions do not have names?
To transfer control to an instruction,Figure 5
the machine retrieves the tag given in the
address part of the instruction, and sets all
TUB's above the location to 0 and all IDB's below
that location to 1. Normal instruction retrieval
(IB = 1, IUB = 1) now yields the desired instruction. To address an instruction as data, one of

AN ORGANIZATION OF AN ASSOCIATIVE CRYOGENIC COMPUTER

the group of control bits called "marker bits" is
activated and sequenced in the same manner as the
ruB, and retrieval is made on the basis of the IB
and this bit position being 1. The data word
which is used as an instruction transfer pointer
can also contain data with no restrictions.
Subroutine processing requires still
another chain sequence control bit. We shall
call this the subroutine argument bit (SAB).
Whenever a subroutine transfer is made, the SAB is
set to 1 below this point in the same ~~er a~
the IUB is set in an ordinary transfer~"lgure ~
When the subroutine takes over a programming,
restriction forces it to retrieve all of its
arguments, which will occur as instructions,
immediately below the point from which the transfer was made. This can be done easily by
retrieving on the basis of the IB = 1 and the
SAB = 1. The reason underlying this requirement
is that if the subroutine in use calls on
another routine, the SAB is then used to retrieve
the arguments for the new routine, destroying the
previous SAB setting. This scheme allows for
saving of subroutine exit histories and intermediate arguments and results so that subroutines
defining recursive functions may easily be
written. The first argument should always
consist of the name of the instruction "to which
control is to be transferred after completion of
the routine just entered. Alternate exits should
likewise be included. The arguments for the
routine are then picked up and transferred to
suitable locations within the routine itself so
they may be addressed without need for address
modification. Each time an argument is retrieved
on the basis of the SAB, the SAB's are reset
down through the previously retrieved word. If
the instructions contain names and not values, as
is likely, then the locations to which they have
been taken can be indirectly addressed, allowing
very flexible argument addressing.
Interrupts create still another problem.
They also imply subroutine action, but they can
occur during the execution of any part of the
program. To enable the machine to restart after
an interrupt, two more bits, called the exception
bit (EB) and exception-used bit (EUB), are named
in the set of control bits. These are identical
in type and operation with the IB and ruB. When
an interrupt occurs, control is transferred to
the correc~ routine and instruction sequenclng
is then carried out based on the EB and EUB", and
not the IB and IUB which are preserved so that
normal operation may commence from the exact
point at which it was stopped. If an interrupt
occurs during the execution of an exception
routine, it is remembered or acted upon based on
the priority it holds over the one being processed. If a more recent interrupt has higher
priority, the earlier one is recorded and the
exception routine pertinent to the later one
takes over.
Addressing
Let us determine what the term indexing

205

means in the context of this machine. Since our
blocks of data are not necessarily contiguous,
and since we have no address decoder, indexing
must be viewed in a different light. An index,
i, enables us to retrieve (or store at) the ith
occurrence of some tag Y. (The tag could be the
tag of the first unused instruction (IUB = 1) so
that we can transfer to "this instruction plus
five," etc.). There are two convenient schemes.
The first is to establish conventional index
registers which can be addressed. The number
needed is not determined, but they would operate
in conventional fashion except that when used to
modify an address, the contents of an index
register would be loaded into a counter and the
tag would be retrieved until the counter hit zero,
marking each retrieved word by setting a marker
control bit to 0 and using a 1 in that location
as part of the tag .( not masked out). At final
retrieval the marks would be reset to allow
future indexing. An alternative scheme is to
allow the marker bits to remain, thus allowing
relative indexing.
But, lnstead of using special index
registers, retrieving any word in storage and
placing its contents in a counter as just
described achieves the same result. Modification
of the word is achieved by an add (or subtract)
one in storage circuit 7 or by performing actual
arithmetic on the word in the arithmetic unit.
The latter is realistic in this sort of machine.
The time needed to access the word can be made
to overlap the other accesses and will really not
be much slower than retrieving a word from an
index register, because access time to registers
is not Significantly faster than from main store
in a cryogenic computer. An enormous advantage
gained in the technique just described is that
every word in the store is effectively an index
register.
As mentioned earlier in our description of
word formats both the address part and the index
address of any instruction may be interpreted in
anyone of three modes: direct, immediate and
indirect. Direct addressing and indexing are
described above. Relative addressing is a form
of immediate addressing in which the index is
interpreted as immediate while the address part
is interpreted directly. Immediate addressing
causes no problems since all that is involved is
using the literal value of the address and/or
index parts of an instruction instead of retrieving on them. An instruction with an immediate
ad.dress and normal or indirect index field iL'uplies

the addition of the final index value to the
immediate address before the latter is used as an
operand value.
Indirect addressing does create a few
problems. To allow complete flexibility with
respect to indexing, the object of an indirect
addressing must be an instruction. Let us consider the case of an instruction with an indirect
address and no index. Since the address is
marked indirect, the machine retrieves on the tag
field finding the desired tagged word and sets a
marking bit to one down through that location.

COMPUTER SYSTEMS

206

Retrieving on the basis of that marking bit equal
to one and the instruction bit equal to one
yields the first instruction following the data
word with the appropriate tag. The address and
index fields of this retrieved instruction now
become the addresses to be used with the operation code of the original instruction, provided
indirect addressing is not implied by the appropriate bits of the new word. If indirect
addressing is implied, then the process described
above is repeated.
To avoid complications, the index part may
be indirectly addressed down through only one
level; that is, if an index part is marked with
an indirect bit, the location retrieved indicates
the location of the index value to be used and
may not be another word of indirect addressing.
However, the word retrieved after retrieval based
on the address part may initiate another complete
indirect retrieval. If this restriction were not
made, an arbitrarily large number of special
registers would have to be created to retain information pertinent to the various levels of
addressing involved in one complex indirect retrieval. It should be pointed out that here, as
in indexing, these operations take considerable
time, each level of indirect addressing requiring
at least one associative retrieval.
Interestingly enough, as one contemplates
using such a device as we are describing here, he
is confronted with new and strange concepts which
for one reason or another never occurred in the
use of previous machines. Suppose one has a
block of data, tagged by the symbol X, stored
throughout the machine, not contiguously, but in
some definite order. The operation store in X is
to be executed. Which X? The first, the last,
a new location? This leads us to the use of two
types of store operations; the first uses the tag
as the name of the existing location in which to
store the information. It can be indexed as can
any other tag. The second type of store is
different from any ever used in a computer. It
says, create a new location with this tag and
store the appropriate data in that location.
Ass~ing that the tag is that of a previously
created block, which new location is to be used?
Can we use one which occurs somewhere in the
middle of the existing block? Probably not. It
is important to retain the block ordering in most
problems even if the elements are.not stored in
a contiguous manner. For example, if a sentence
of English were to be translated into Russian aIlQ
we stored it 1h~der one tag, and then decided to
add to its tail, it would be of no use to store
the additional material within the limits of the
block. Confusion would be the only result. To
enable us to get out of this difficulty, we establish a set of rules and a pair of new hardware
features. The rules say, load the program and
data in one contiguous mass, with no intervening
available locations allowed (although empty
tagged locations are certainly permitted). Whenever a location has served its usefulness and it
is desired to remove it from consideration, set
its availability bit (AB) to 1. All retrievals

are made with the tag having availability bit set
to 0, and all locations which are unused but at
the tail end of the store have their availability
bits set to 0 as do all initial program and data
words.
It is possible to attempt to store information in a new location and find none available.
To permit the locations which have their availability bits set to 1 to be used would result in
confusion, but the presence of these unused
locations is tempting. If storage is attempted
and no location is available, we shall determine
that this results in an exception condition and
an appropriate automatic interrupt. At this time,
storage is read out onto some 1-0 device
(hopefully a high-speed disk) being retrieved on
the basis of a zero in the AB. Thus only active
words will be read out. The device then writes
its contents back into storage, but in consecutive
locations, so that all unused words effectively
disappear. The AB positions are all set to 0 and
operation of the program is restarted where it
left off. In the event of two consecutive
failures in attempting to store in a new location,
the program is obviously too long or hardware is
at fault and appropriate action is taken.
Sequencing Control Summary
Our machine has no location counter, but
substitutes a set of bits in the control part of
the word for this feature. The instruction
format allows two full addresses: one for the
data itself, and one for an index to modify the
data tag. Either or both of these may be indirect,
immediate or direct, depending upon the setting
of four bits associated with each instruction.
Indexing is seen in a new light and another
control bit (the marker) is provided to facilitate
this operation. Blocks of storage cause some
problem since their order is important but they
have no assigned limits. An additional control
bit, the availability bit, is used to control
storage availability and prevent the disordering
of stored arrays.
Input -Output
Control word 1-0 as implemented on the 709
and 7090 seems ideal for this type of machine.
What is needed is another "counter" which will
mark those words "retrieved for output" or "used
in input." This will take the form of another
chain seQuence control bit called the input-output
bit (rOB). It will function exactly as does the
TUB and its equivalents except that it is under
control of the input-output exchange and not the
central processor. Using proper tag control,
individual words, blocks of data, blocks of instructions or the whole memory can be read or
written into. Indexed input and output provide
some problems, but they are surmountable. Linear
blocks are read in, either in new locations or
into words with previously created tags, in a
manner analogous to simple store operations.
Reading them in backwards provides a problem,

207

AN ORGANIZATION OF AN ASSOCIATIVE CRYOGENIC COMPUTER

but this can be met by having the control process
the IOB se~uencing in the inverse direction.
Picking up scattered words is messier since the
use of a se~uence-type bit demands linear order,
but subroutines which establish a proper control
word se~uence can be produced with no exceptional
difficulty.
The problem of faulty 10 transmission can
be met by using the same control marker bits which
were used to mark the transmitted words. If a
check sum is in error, the routine will have
access to the words in storage and can either
erase them (make them available) if they were
read in, or reread them if they were read out.
At the end of a successful 10 operation, the bits
are set back to 0 before starting a new control
word. If, during a write se~uence under 10
control, there exists a situation in which no
locations are available, the machine should
interrupt as usual, but retain all of the control
information in a frozen state while the remedial
read-out write-in routine described earlier is
performed. This implies that we have a machine
which is at least two machines in one in that
either one can interrupt the other in certain
situations.
Multiprogramming Considerations
Multiprogramming, which has became a desired feature of new systems, can be accomplished
in a very straightforward manner in a machine of
our design. Suppose we assign eight of the
control bits to a special heading character.
Each processing unit which is to have access to
the store automatically applies its heading
character to the proper area during retrieval.
If concurrent operation is desired, extra read
and write lines can be provided. Each processor
re~uires its own IB, TUB, etc.
Certain routines
can be common to several programs and data areas
can be also. Data areas can have their heading
character changed so they may be, in a sense,
transferred to another processor. Interprogram
protection is provided by these characters, and
words used by several programs can be mixed indiscriminately with no harm. Common subroutines
must make themselves available to only one main
routine (contained in a separate processor) at
one time. The executive routine must provide
priority scheduling to determine which routine
can force another out of a subroutine temporarily
for its own purposes.
In systmms of multiprogranuning where simultaneous processing units do not exist, the system
proposed above will still suffice. If the executive routine is given a message saying that
program A is to supersede program B then the
active heading character is changed and processing commences on B while A sits idle. If A
is not needed its words may be marked by the AB
and the storage can be compressed at a later time.

Table Look-up
Table look-up as a fundamental operation
implies the following in a machine of contemporary design. Given an argument, find a corresponding entry in a table (either an e~ual entry,
or one greater than or e~ual, etc.) and from a
parallel table derive a result on the basis of
the location of the original argument in the
first table.
Central to this concept is the ability to
compare an argument with a number held in storage
and return a signal depending upon whether the
result is high, low or e~ual. Circuits to
accomplish e~ual comparison exist as part of an
associative store. 2 'The programmer merely must
adjust the retrieval mask to allow for the argument as well as the tag. High and low comparisons
are not so easily achieved, but are feasible.
To facilitate the implementation of some of
the ideas presented on table look-up and retrieval
of data based on complicated criteria, a system
of marker bits would be most helpful. For
example, to find the first ")" after a letter, it
would be sufficient to find each ")", marking it
and all words below it, and then do an indexed
retrieval based on the marker bit condition desired. A set of machine commands to enable these
operations should be investigated.
A look at some of the ideas mentioned above
leads one to believe that retrieval might not
only be indexed, but might be programmed to set
the index counter to the index of the word in
which the desired argument is found as in table
look-up. This could be a slow operation since
retrieval is normally a parallel operation. This
looks like a macro which retrieves the tag and
then tests the result, adding one to the counter
each time the operation is performed.
Mask Control and Retrieval Tags
We have alluded to two types of retrievals;
one in which the hardware of the machine determines the fields to be retrieved upon the instruction contains the desired tag allowing the instruction se~uencing control to set up the
necessary mask and condition, and the other in
which the programmer determines the masks and
fields to be used. It must be possible for the
programmer to have access to any part of a word
without too much difficulty, especially since he
must be able to program input and output of full
words including control and marker bits. This is
not so simple as it sounds since ordinary processing is concerned with the right-hand part of
the word (excluding the control bits) only, and
for this sort of work there is no need for access
to these areas.
A solution to this problem is foun~ in the
fact that seldom, if ever, is more than the body
(less the control bits of a word) used for tagged

COMPUTER SYSTEMS

208

retrieval. In our system we shall stipulate that
this is never possible. Retrieval based on uncommon tags and masks (such as to find the location of the first word which has a certain marker
bit set to 1) can be accomplished in the followillg way-.

Tl1ree 111stl-'uctiorlS should exist in the

machines: one which specifies the word used for
retrieval tag, one specifying the word used for
masking purposes, and the third commanding the
actual retrieval along with an appropriate offset
to the left to be applied to the mask tag combination. Bits to the right (shifted out of) are
automatically masked out, as are bit positions to
the left which are not shifted into. In actual
use, these instructions would be combined into
macro instructions to enable the programmer to
handle special functions based on the control
bits as if they were hardware operations built
into the device. The operations would also be
available for the programmer to use to build up
his own macros.
In normal operation, the rightmost 115 bits
of the word can be retrieved as a group and can
be conveniently checked for errors. If the proper
number of checking bits are provided, error
correction may be implemented very easily. However, the chain bits create a problem here too.
Since the chain bits may change in storage without being brought into the arithmetic unit,
forming parity sums, etc., is quite difficult.
For this reason, checking and correcting bits
would not apply to chain bits. If a word in
store is found to be defective, a control bit is
set to zero. This bit is called the disabled
bit (DB). It consists of a persistent-current
loop which always contains a binary 1. If a
word is found to be faulty, this bit is set to 0
by forcing enough current through the loop associated with the bit to fuse the metal in the loop
so that it may never be reset. All operations
in the machine will be masked so that any word
used must have a binary 1 in this bit position.
Since words need not be stored contiguously in
an associative store, the memory is still
functionally the same as before except there is
one less word availab~e for use. When a memory
unit contains too great a number of words which
have become marked with an 0 in the DB then the
entire segment of the storage must be replaced.
A routine which reads this bit and counts the
number of occurrences of an 0 in the DB location
will determine when this condition is met.
Systems Programming Considerations
The two most important functions which a
translator must perform are scanning and table
building. This is true independent of the type
of translation; assembly, compilation of macro
or algebraic language, interpreter translation,
etc. Table building is a straightforward task
in an associative computer because each table
entry is accompanied by the table name. Multiply
dimensioned arrays can be bl1ilt using the listof-lists technique. The scan is a different
matter: but the hext few thoughts sho')~(1 explain

how it can be easily accomplished in a machine
such as we are discussing. A full scan usually
implies examining the source input for functional
groups, extracting these and adding them to the
proper tables, and then performing some sort of
translation on all or part of the material and
inserting the result into further tables. For
example; in a compiler the scan might isolate all
variable names, function names, statement labels,
operations, etc., tabulate these and then put out
a list of intermediate machine operations which
would be later translated into machine code. The
problem of assigning locations and regions to
variables is nonexistent in an associative-store
machine, so there is not too much of a problem
in putting out machine code after the first scan.
The problem is that one must be able to write a
program 'Nhich can isolate functional units in an
easy fashion; look for delimiters, other punctuation and operations. Fortunately this provides
no great problems.
If the words contain only single characters
as suggested then it is a simple task to retriev~
not the ith occurrence of X, but the first or ith
occurrence of X containing "," followed by")"
is not so simple and must be programmed by finding
the index of the comma and determining if the
next character is the ")". Other such complicated detections are similarly programmed using
marker bits. Finding the first ")" preceded by
a letter is not simple i f each letter must be
compared with the retrieved character. For this
reason, a character set might be devised in which
letters, numerals, punctuation, and special
characters could be distinguished on the basis of
two common bits. The mask control and the proper
retrieval criterion could enable this task to be
programmed and performed easily.
The question arises as to how one would
implement a list system in an associative cryogenic store. In one scheme, marker bits are
kept to indicate the sequencing of words in a
sublist. Tags would have to be provided to serve
as branch points. The mode of sequencing would
determine the masks to be used during retrieval
as affecting flag bits and other parts of the
data word. Note that the existence of an
availability table is unnecessary.
An alternate scheme is to give each word a
distinct tag and to implement a scheme similar
to that used by Newell, Shaw and Simon, except
in a more general way. In this case a partial
mask is used on the tag field during normal
retrieval but removed for finding successor and
predecessor elements. The words tagged with
augmented information contain the tags of the
first preferred immediate successor and immediate
predecessor elements, the tags of the second
preferred, etc., one word for each level of
successor and predecessor tags. Alternatively,
the words associated with one data word could
have the identical tag and the ith retrieval
could retrieve the (i-l)th level of successorpredecessor tags "f.·[herl used

~.~ri th

proper marl'\.ing

control.
It might be pointed out that

COrrL.~on

Yl1.lrneric

AN ORGANIZATION OF AN ASSOCIATIVE CRYOGENIC COMPUTER

addressing is possible using associative techniques. In this case a tag field is devoted to the
numeric addresses which are fixed for all time
and used associatively to find the word with the
numeric tag of n. This is a slower scheme than
others but provides some generality in an associative store since it is easily simulated in such
a device.

References
1.
2.

3.
Conclusions
There are arguments on both sides of the
issue of whether an associative cryogenic computer should be built. The arguments against
such a venture center around the fact that perhaps the expense involved in the organization and
construction of the memory circuits could best be
used more directly in the design of a computer if
the memory and hence the entire machine were
simpler. However, there are advantages to this
design which might be pointed out in order to
better evaluate the machine. Let us mention a
few.
The complexity in the memory logic as described in this paper diminishes the need for some
of the complexity in the control circuits, hence
fewer different masks are needed when preparing
circuitry. Due to the difficulty expected in
maintaining and repairing a cryogenic computer,
the iterative character of the circuitry involved
becomes advantageous also. This, coupled with
the disabled bit (DB) scheme, decreases the
problem of maintainability.
The associative property of the memory
allows the machine to be used so that symbolic
names in source language programs need not be
translated into numeric addresses. Table entries
are determined by order and relative to a tag,
thus these need not be contiguous. This diminishes the storage allocation problem to a very
great degree. Moreover, the corresponding pass
in an assembler or compiler is not needed,
resulting in a real saving of computer time.
The general power and flexibility of an
associative mem.ory are not diminished at all in
this design. Such operations as table look-up
and list processing can easily be achieved in
this computer as can compiler statement scanning,
and many other functions. Thus, for some purposes associative memories promise to be better
organized than conventionally addressed arrays.
The advantages of cryogenic circuitry have
not yet been fully demonstrated, however, the
prospects ~or several benefits in this area are
quite good. These include relatively fast
switching time and compact construction. The
cost of a machine built of these components
should be low once the masks used for depositing
the circuit material have been produced. The
fewer the masks, the lower the total cost. The
associative cryogenic machine, with a great deal
of its logic in memory will benefit from this
standpoint.

209

Kiseda, J. R., et al, "A Magnetic Associative
Memory," IBM Journal, Vol. 5, no. 2, p. 106,
1961.
Seeber, R. R., "Associative Self-sorting
Memory," Proc. Eastern Joint Computer Conference, 1960.
Seeber, R. R. and Lindquist, A. B., IIAssoci_
ative Memory with Ordered Retrieval," IBM
Journal, Vol. 6, no. 1, p. 126-136, J~1962.
Slade, ft... F., McMahon, H. 0., "A Cryotron

5·
6.

7.
8.

9·

Catalog Memory System," Proc. Eastern Joint
Comvuter Conference, p. 115-119, 1956 •.
Slade, A. E., Smallman, C. R., "Thin Film
Cryotron Catalog Memory, II Symposium on
Su erconductive Techniques for Computing
Systems, May 1 O.
Buck, D. A., liThe Cryotron - A Superconductive Computer Component, It Pro. IRE, Vol. 44,
no. 4, p. 482, 1956.
Haynes, M. K., IICryotron Storage, Arithmetic
and Logical CirCUits," Solid State Electronics
Vol. 1, p. 399-408, Sept. 1960.
ROSin, R. F., "Cryotron Circuits and Memories~!
Course on Theory of Computing Machine DeSign,
University of Michigan Engineering Summer
Conferences, 1961.
Slade, A. E., "A Cryotron Memory Cell, II Proc.
IRE, Vol. 50, no. 1, p. 81-82, Jan. 1962-.-

COMPUTER

210

BITj

SIDE
I SIDE
+1
i
.-4------1-,
I
I

I
WORD i -I

BITj+1

~.i------~= I

I \ .•

I
I

I
I
I

I,'
I

L _____ J

11--1-- :

r ------l
I
I
I

W:
'-r----

iW
I

~-----l

I
I

-- -- I

I
I

I
I
I
L ______ J

L _____ J

CHAIN

BITS

'-1--------'

-I

WORDi+1

I -

Lt---- J

WORDi

PERSISTENT CURRENT

LOOP CELLS
FIGURE 1.
ASSOCIATIVE
MEMORY CELLS

SIDE

I SIDE

+ --R EAD
-=r::

ASS OCIATE

---+
ASS OCIATE

---+

FIGURE 2
ASSOCIATION CHAIN 81 T

SYSTE~S

211

AN ORGANIZATION OF AN ASSOCIATIVE CRYOGENIC COMPUTER

MA SK LINE
(CU RRENT=I)

~ISIDE

SEQUENCE

READ i-I

+
)
v

I SIDE ~

"./)

)

..-

READi

'--

ASSO CIATE
--+

ASSO CIATE

---..
SEQUENCE CHAIN BIT
FIGURE 3
SEQUENCE CHAIN BIT

DATA WORD CONTROL BITSf

TAG

r +25

DATA

2~~15 "I" 64 --48-=--=--=-:~~2

INSTRUCT~NI~CO-N-ffi-O-L-B-IT-Srl~A-D-D-R-ES-S~PA-R-T~~I~¥-p-C-O-DE~I~~~IN-D-E-X~~~~ll
WORD
~
'i
'INDIRECT AND IMMEDIATE BITS/

FIGURE 4
WORD FORMATS

COMPUTER SYSTEMS

212

CONTROL

BITS

IUB

0
0
0
I

I
0
I
I
I
0
0

MAIN

BODY

ADDRESS

ALPHA

TRA

ALPHA

........

I
I

OP CODE

ROUTINE
ALPHA

FIGURE 5.
INSTRUCTION SEQUENCING

CO NT ROL BITS
IB

IU B

0
I
I

0
0
0
0

MAIN BODY

SAB

0
0
I
I

SUBROUTINE TRANSFER OP

ARG I
ARG 2

~
I

BODY OF SUBROUTINE

FIGURE 6.
SUBROUTINE TRANSFER 8
DATA RETRIEVAL

213

INTEGRATION AND AUTOMATIC FAULT LOCATION TECHNIQUES
IN LARGE DIGITAL DATA SYSTEMS
Donald W. Liddell
U.S. Navy Electronics Laboratory
San Diego, California

summary. A digital computer, if used with
proper programming techniques, can be a powerful tool during the processes of physical
integration of complex digital data processing
systems. After system integration, as such,
has been completed the same techniques may
be used to provide performance monitoring
and daily calibration status data for all or
any part of a system.
Investigation of such programming techniques
during system integration of the Developmental Navy Tactical Data System (NTDS) at USNEL
produced results which indicated the possibility of using the computer for automatic
fault location in the system. Some progress
has been made in this area, and a program
which allows the NTDS computer to identify
a failing logic card associated with its own
memory logiC and switching circuitry has been
successfully demonstrated. The final objectives of this approach are to provide facilities to perform on line performance monitoring
and automatic fault location, reduce to a
minimum the external test equipment required
for a system, and eliminate insofar as
possible the high degree of training presently required in the system maintenance
technician.

Within the past few years the digital computer has developed from a large, unreliable
device into a relatively small package of
solid state elements, with fairly good operational reliability. There has, naturally,
been a revolution in military real-time data
processing systems encouraged by this dEvelopment. General purpose stored program digital
computers and peripheral equipments comprising a system for modern practical data processing are now conceivable in a size suitable
for shipboard, aircraft or other vehicle installation. Figure 1 is a block diagram of
a typical system.
Along with these new systems a new variety of
systems problems has arisen, and one of the
first and most important is the fact that the
"systems engineer" is suddenly too narrow-

minded to cope with the new systems concepts.
In the past the systems engineer has been a
man with a broad background of knowledge which
enabled him to make a complicated complex of
equipments function as an integrated unit.
However, he is now faced with the fact that
this "complex of equipments" is just one black
box in a jungle of black boxes which must
function together in real time as a new
"super system II. The real problem here is that
he does not recognize this fact. His approach
is to make sure that his portion of the system
is functioning according to some over-all
speCifications, then wait for the mysterious
process of system integration. When, in fact,
an attempt is made to achieve operation with
his device in conjunction with other systems
units, and complete failure occurs, his reaction is to retire to his own device, check
it out thoroughly and proclaim that it is
functioning properly while pointing his finger
in the approximate direction of the remainder
of the system and making disparaging remarks
about its obvious inadequacies.
At this point, it should be pointed out that
computer programs, although referred to as
"software", are in fact hardware in the same
sense as any other piece of system equipment.
The idea of classifying programs as "software"
and placing them in a separate category is
repugnant. Programs are indeed among the
'~ardest" of those devices encountered in
system integration. In fact, the computer
program is quite analogous to an electronic
system unit, i.e., it requires design, performs
a function, and requires readjustment after
initial design in order to perform in a realtime environment. The term "program debugging"
is particularly noxious as it implies the
location of minor clerical errors. Nothing
could be further from the truth. The programmer vigorously pursues this "debugging
function" by placing patch upon patch in the
operational program, interrupting these processes frequently with cries of 'we've obviously got a hardware problem!" Meanwhile, a
final operational program is assembles which
will consist of one computer instruction and
30,000 patches. Frequently, when these alleged
'~ardware problems" have been resolved to be
an illegal series of computer program

214

instructions, it becomes obvious that the computer programmer concerned has been subjected
to a gross underexposure to system interface
circuitry and timing characteristics.
The foregoing can be described as problem
number 1 -- System Integration.
Assuming that system integration has been
accomplished -- that is, we have a large group
of computer and other system components and a
working real-time operational program -- the
next phase in a developmental system is one
of Operational Evaluation. This is where we
find out whether the system performs according to specification and, in fact, to what
degree it ~~fills desired practical functional requirements. While failures and incompatibilities are noisy and catastrophic during
the Systems Integration Phase, they are more
subtle but nonetheless catastrophic during
the Operational Evaluation Phase. Individual
equipments drift out of tolerance, program
patches cause nebulous functional changes in
the operational program, operators of systems
components, bored with long periods of inefficient operation, discover unique ways of
causing the system to fault and, as a result,
days and in many cases weeks of operational
testing are lost or wasted. Quite frequently
when magnetic tape recording is the only means
of data gathering for analysis, and when
analysis of data is performed at a later date,
it is obvious that the fact that the eqUipment
in the system was not functioning properly is
not discovered until it is too late and tests
must be re-run.
The foregoing can be described as problem
number 2 -- System Calibration and Performance Monitoring.
up to this point in development and from this
point on, we have and will be faced with the
physical failure of sub-system components.
Components are defined as cards., modules and
other such small replaceable units. It is
obvious that even a simple failure in a
system such as that shmm in figure 1 can be
catastrophic. Such a failure in one portion
of the system can manifest itself as an ailment apparently in a different part of the
system, and many hours of time have been
spent by people with intimate knowledge of
the circuitry involved and using conventional
test equipment before the ailing element was
found.
If large scale data processing systems such
as NTDS are to operate in real time, and real
time includes 24-hour a day operation with no
appreciable time out for preventive maintenance, it will be necessary to have facilities

COMPUTER SYSTEMS

available for rapidly locating the failing components in the system while system operation
continues.
The foregoing can be described as problem
number 3 -- Automatic Fault Location and
Diagnostic Techniques.
A general purpose digital computer is the controlling device in a digital data processing
system such as has been described and is an
excellent tool in solving the problems in the
aforementioned three problem categories.
During the integration, development and operational testing of the Navy Tactical Data
System, efforts in the first two problem areas
resulted in computer programs which exhibited
characteristics that led to the belief that a
solution to the third problem was possible.
During the process of system integration it
became obvious that there would be computer
failures, interface problems such as timing
and logic level differences, incompatibility
of different types of circuitry used by various
contractors, incompatibility between operational computer programs and equipments, etc.
The first effort was in the computer area,
various command, memory, arithmetic, input/
output, frequency margin, etc., tests were
written. Figure 2 shows the original method
of taking frequency margins on the computer.
Two technicians were required to perform this
function; one to operate the computer and the
other to make adjustments of the one megacyle
clock and observe waveforms on the oscilloscope.
As the clock frequency was adjusted to one
margin, the computer would fault and the period
of the clock would be measured on the oscilloscope. This would be recorded, the program
restored by the technician at the console and
the process repeated for the other frequency
margin. This process quite frequently resulted
in the dip stick, held by the technician,
destroying several cards in the computer and,
as can be imagined, the results are not too
accurate. A program was written which allowed
the computer to make its own frequency margin
measurements. The only thing required of the
technician was adjustment of the clock frequency control from one extreme to another and
the program would cause the computer to dump
its margins on the flexowriter. A sample dump
is shown in figure 3. This test resulted in
reduction from about 10 to 15 minutes for frequency margin checking to about 1 minute. An
executive program was written which allowed
all computer maintenance tests to be stored
on magnetic tape and automatically called up
for execution during preventive maintenance
periods. Interference by the technician is
necessary only if there is a typeout indicating
trouble. Very shortly, as system integration

INTEGRATION AND AUTOMATIC FAULT LOCATION TECHNIQUES IN LARGE DIGITAL DATA SYSTEMS

continued, it became necessary to write
simple minded display console and other subsystems computer test programs to assure that
these devices were functioning in a gross
manner with the computer and with each other.
Figures 4 and 5 are PPI presentations of
patterns resulting from some of these types
of tests. Figure 4 is a category selection
test in which symbols appear on the PPI in the
same relative position as their selecting
buttons appear on the console panel. Obviously, the presence or absence of a symbol at a
particular time will pinpoint a fault. T"ne
figure shows various combinations of category
selections. Figure 5 pres~nts four other
system integration type tests. Figure 5A is
a function code test where an action button
in a system unit is actuated and its associated function code (in octal) is sent to the
computer. The function code is checked in
the computer and sent back to the system unit
where it is displayed for visual check by the
unit operator. The spaces between the horizontal row of crosses represents the digits
1 through 6. The function code shown is 56.
Figure 5B is a velocity leader test, 5C is a
range ring linearity test, and 5D is a primitive position accuracy test. These and other
tests have been incorporated under an executive routine which allows them all to be run
concurrently in the computer, then selected
individually at any system position. This
type of test helped innneasurably during the
processes of physical system integration.
The term "physical integration" is used
because the phases of system integration and
operational evaluation necessarily overlap
somewhat.
upon entering the operational evaluation phase
it became painfully obvious that it would not
be possible to do a realistic job of evaluation without some means of system calibration
and performance monitoring. Computer calibration type programs were written for various
system configurations and were eventually incorporated under an executive routine for use
with the complete system. These programs are
now written on a magnetiC drum· for purposes
of fast access. Any of the programs may be
loaded in the computer in a matter of 1 or 2
seconds, and automatically executed. If a
different test is desired, it may be called
up by inserting its identifying number into
the computer. The currently running test is
interrupted; the desired test is automatically loaded and executed.
Figures 6 through 8 describe one of these
types of calibrative tests. Figure 6 is a
block diagram of the particular system configuration concerned. Included are a video
processor, a unit computer, an NTDS display

console, and the prime reference in the form of
the USM/94 radar simulator. The simulator has
two outputs; one is rho theta analog video
output, the other is XYH components, in digital
format, corresponding to the instantaneous
values of rho theta. These XYH components are
sent via a digital readout buffer (DRB) to the
unit computer. The purpose of this test is to
provide positional information calibration for
the complex shown. Targets are generated in
the USM/94 whose original positions have previously been written in the computer memory.
Hence, a comparison with the DRB information
(2) will verify whether simulator information
is correct or not. The rho theta analog video
(1) to the video processor is reported by the
processor (3) to the unit computer where,
again, a comparison can be made. The rho theta
analog video (1) is applied to the NTDS display
console and appears as PPI video. A console
operator can enter a symbol over what appears
to him to be the target position and this information is sent (4) to the unit computer.
Each of the aforementioned pieces of information (2, 3 and 4) are caused by the computer
to be displayed as distinctive symbols on the
NTDS display console PPI as shown in Figure 7.
If everything in the complex is indeed in
calibration, all symbols and video will be
exactly superimposed and the person responsible
for operational tests for the day can quickly
determine whether system accuracy is adequate
for his purposes. The symbols at the twelve
o'clock position of Figure 7 are purposely
separated to show what erroneous system adjustment would look like, and to identify the
various pieces in the arrangement. The half
box symbol positioned over the video is the
DRB report. The half diamond symbol is the
video processor report and the small circle is
the operator's interpretation of the target
position. The simulator provides for approximately 32 tracks in an infinite variety of configurations. The tracks can, in fact, be
moving and a record kept. However, this has
not been found to be necessary. Several pieces
of video do not have symbols associated with
them as this is selectable by program. Once
all the information is inserted in the computer,
a dump can be made which serves as a calibration curve to show the equipment condition on
that particular day. An example of the computer typeout is shown in figure 8. If the
system is in perfect calibration the corresponding X and Y values for the three sources of
coordinates on the top half of figure 8 should
be identical and it follows that the three
groups of differences in the bottom half of
figure 8 should all be zeros. This particular
dump was chosen because it shows some gross
discrepancies, and, in fact, these discrepancies tend to point out the areas where there
are systems problems.

215

216

This type of calibration test has been invaluable during operational testing of the developmental NTDS. In fact without it, evaluation
would have been impossible.
The progress made and results obtained from
the computer program tests written to help
solve the problems of system integration and
operational eValuation encouraged a look into
the problem of fault location. Fault location
and maintenance can be extremely t\ifficult,
but conventional methods can be d~sastrous;
fingerpointing runs rampant while the system
remains useless. The primary objective is to
eliminate insofar as possible the difficulties
associated with fault location and maintenance.
It is true that a group of highly trained
technicians can maintain a large system, provided they have extremely good documentation,
good test equipment and good systems engineering leadership. However, if one can designate
a single equipment in the system such as the
display console as having failed, then a good
technician with good documentation and good
test equipment can repair it. If indeed one
can designate a single drawer of logic as
having failed, then a relatively poor technician with good documentation and test equipment can repair it. Further, if one can designate one row of cards as having a failure in
it, a technician with a chassis map and a card
tester can repair it. Finally if one can
designate one card as having failed, then
replacement is all that is required. So the
trick is to ?JlOW when a failure is present
and to pinpoint its location -- Automatic
Fault Location.
There are two ways to automatic fault location. First, the so-called maintenance console which is being pushed by many organizations and indeed may have a place in systems
which are not expected to work in real time.
However, if they themselves are simple devices,
they are inadequate to perform the function
of fault location in large scale systems.
And, if they are sophisticated enough to perform the required function then they themselves
require another maintenance console in order
to determine whether or not they are functioning properly. This approach for any system
which has a general purpose digital computer,
or in fact a wired program computer associated
with it, should be opposed. The second way
to automatic fault location is to use the
digital computer which is the controlling
element in a data processing system as the
diagnostic and fault locating tool. Assuming
that the computer can be used as the standard
and the fault locating tool in the system,
and since the memory is basic to the computer
a computer program should be devised which
will allow the computer to find a bad logiC

COMPUTER SYSTEMS

card in the logic and switching circuitry
associated with its own memory. One method
for performing this function with conventional
external test equipment is shown in figure 9.
The machine in the center of the picture is a
memory chassis tester. The device held in the
upper half of the machine is a memory chassis
from one of the NTDS unit computers. In
reality, two technicians are required to perform maintenance and fault location on this
device; one, as shown, observing waveforms and
the other on the opposite side of the machine
pushing logic switches. They go through a
logical process, observing vTaveforms until
they find one that does not conform to specifications. This process can take anywhere from
several hours to several days for completion.
The objective is to eliminate the two technicians, the memory chassis tester and the
oscilloscope and to reduce the time factor to
a matter of minutes. Figure 10 illustrates
the logical processes gone through by the two
technicians in the use of the memory chassis
tester. The column of XIS and lIs on the left
indicate the functions of one technician, and
the logic tree is followed by the second techn~c~an.
At each point he reaches a decision
and follows an arrow to the next position.
Eventually he finds a bad card. This is one
of many such logic trees that are used in conjunction with the memory chassis tester. It
is obvious that this sort of logical procedure
should be adaptable to computer implementation.
Since the first NTDS computers were experimental, no physical facilities for implementation
of automatic fault location (sensors) was provided. Consequently the approach was to make
a complete analysis of all memory logic -define all possible failures and determine for
each failure what the reactions would be for
various stimulation patterns. A program was
written which analyzes the reactions and points
out the failing logic card. This turned out to
be approximately an 8-man-month effort; however,
when it was successfully demonstrated it was
felt that a large step had been taken in the
direction of completely automatic fault location
in digital data systems. The fault location
program itself runs a variety of patterns; all
zeros, all ones, alternating twos and fives,
and randomly generated words. If there are no
faults in the memory logic, the program takes
approximately 20 seconds to run. If a fault is
encountered the running time is proportionally
shorter. When a fault is encountered, the computer will identify it by way of flexowriter
output. A typical typeout is shown in figure
11. The typeout indicates in which pattern the
test failed; in this case, zeros. The next
line indicates a bit picked up. The next line
indicates the area in memory where the bit was
picked up, and the next three lines offer
suggestions for the maintenance technician to

INTEGRATION AND AUTOMATIC FAULT LOCATION TECHNIQUES IN LARGE DIGITAL DATA SYSTEMS

follow. The first four figures in each of
these lines indicate the card type that could
have failed (021A, 020A, 022B). The next six
figures indicate a chassis and the cartesian
coordinate location of the card on that
chassis (for the first suggestion, J14 =
chassis 14, B = row B, and 34 = column 34).
Normal procedure would be for the technician
to take the first suggestion and interchange
these two specified cards. If, upon running
the fault location program again, the trouble
follows in the typeout as indicated by the
arrow on fig~e 11, it is obvious that there
is a bad card in that location, i.e., chassis
14, row E, column 34. If the typeout does not
change, the technician takes the second suggestion, and so on, until the trouble does follow
card changes in successive typeouts. There
are a couple of other suggestions made; however, in just about every instance it will be
a card failure. The program will cope with
multiple faults. It merely takes them one at
a time. When the first fault encountered is
corrected the computer then proceeds on to
the next. It should be noted that in a
tactical situation all computer suggestions
would be implemented at once.
What the development of this type of program
amounts to is a tremendous job of circuit
analysis; however, this could be simplified
in future systems if provisions for sensing
are included in the design. In the final
analysis, what is being done is to let the
systems engineer and computer do all of the
maintenance technician r s thinking for him.
This memory test itself actually occupies only
a small portion of memory and its one drawback
at the present time is lack of mobility. However, it is not felt that it will be difficult
to devise a probling program to find a clear
space in memory in which to place the test.
If, indeed, there is more than one computer
in the system, as is the case in NTDS, we can
use this program in one computer to automatically perform fault location in the memory of
the other computer. The only requirement
here is that there be three functioning
addresses in the memory of the ailing computer. At present there is an effort in
accomplishing an analysis of the arithmetic
section of the computer and writing a program
for fault location in this area. other blocks
of the computer will be taken tor analysis as
time allows.
Concurrently, an effort is being made to use
the computer in automatic fault location for
the remainder of the system. Two approaches
are being pursued; one is to stimulate and
observe reactions, as described in the previous test, the other is to duplicate the

217

logic function of the external device in the
computer memory and exercise both simultaneously while sensing any difference. The final
program will probably be a composite of these
two approaches.
It is obvious that the type of person we need
to write this type of computer program is not
the usual computer programmer. He must be
several things. First of all, he must be a
good circuit man, he must understand computer
operations, he must be an overall excellent
system.s llian of the more broadrninded variety,
and, incidental to this, he must be an extremely clever computer programmer. There are very
few of this type in existence today.
What would be desirable to have as a final
product is shown diagrammatically in figure 12.
Actually, the computer memory would be filled
almost completely with operational programs
and the test and executive routine would
require a minimum of memory space. The
"current test II the majority of the time would
be merely a performance monitoring test -- a
problem-solving routine. Periodically, the
system is asked to solve a problem and, if
indeed the answer comes out correct, everything
is apparently normal. However, upon receiving
an erroneous solution to the problem, the
executive routine would cause a diagnostic
program to be called in from high-speed storage
which asks the question, I~ere, on a subsystem basis, is there trouble?" Once this
has been defined we can degrade operation of
the system; that is, use a simpler operational
program which does not include the offending
equipment. This will give more space in memory
for the more sophisticated automatic fault
location program. The fault location program
would then be called into the computer and
would locate the failing component down to the
smallest replaceable unit level. This, of
course, assumes maximum system operation requirement all the time. There will, of course,
be periods when full operational capabilities
are not necessary. During these periods on-line
maintenance and diagnostic routines could be
performed.

In the afore described test programs probably
the most important factor is that they be
written in a manner which causes the system
equipments to be exercised in precisely the
same manner as is done in the system operational program. One or the other must be altered
in order to conform. Any other approach obviously makes test results meaningless.
Up until the very recent past, it
tremely discouraging to· talk with
systems people around the country
ject. There has been very little

has been exvarious
on this subenthusiasm

218

for this type of effort. The main concern
seems to be with a type of program which is
designated as an "exercising program" whose
sole function is to exercise a piece of equipment in some fashion for a given period of
time. If the equipment indeed passes this
test, it is assumed ready for delivery, and
acceptable for use in a system. It has only
been more recently that it has been realized,
or perhaps admitted, that this is not a
reasonable way to approach the problem.
There is growing opinion that the types of
programming techniques described in this
paper are absolutely necessary, if there are
to be large scale data processing systems
which are capable of working in real time
continuously. Results have been encouraging
and it is hoped that other systems people will
consider their merits.

Reference
'~e Development of a Rote Diagnostic Process
for the Atlas Guidance Computer System",
H. R. Nonken (Burroughs), Vol I, Proceedings
of the Fifth AFBMD-STL-Aerospace Symposium,
August 1960.

CO~PUTER

SYSTEMS

219

INTEGRATION AND AUTOMATIC FAULT LOCATION TECH;\;IQUES IN LARGE DIGITAL DATA SYSTEMS

RADAR
OR
SIMULATOR

)('Y,H
DIGITAL

COMM.
INPUT-OUTPUT
~"

,.
-

ANALOG

---

COMPUTER I

...

COMPUTER 2

DISPLAY
GENERATOR
j~

I-----

,
/J&

+
,Ir

jll

VIDEO
... PROCESSOR

AUXILIARY
EQUIPMENT

,r
.-

ORB

PERIPHERAL
EQUIPMENT

DATA
RECORDING

Figure 1 - Typical Data Processing System Configuration

PERIPHERAL
HARDWARE
20-30 UNITS

220

COMPUTER SYSTEMS

NT OS

.962 MEGACYCLE

1.040 MICROSEC

1.133 MEGACYCLE

.882 MICROSEC

Figure 3 - Flexowriter Typeout of Automatic Computer :'Crequency
lJIargin Test

Figure 4 - Category Selection Test

INTEGRATION AND AUTOMATIC FAULT LOCATION TECHNIQUES IN LARGE DIGITAL DATA SYSTEMS

Figure

5 - Miscellaneous Display Tests

(f)

,,0& (ANALOG)

USM 94
SIMULATOR

X, r,H

(DIGITAL)

VIDEO
PROCESSOR

NTDS DISPLAY
CONSOLE

@
..

ORB

UNIT
COMPUTER

--'@
~

---

,Ir

CALIBRATION DUMP
Figure 6 - T;ypical Sub-System Configuration

221

COMPUTER SYSTEMS

222

Figure 7 - PPI Presentation of SUb-System Calibration Test

TRACKING ACCURACY-CALIBRATION OF VIDEO PROCESSOR AND NTDS DT/S
TRKNO

X(USM-94)
miles

Y(USM-94)
miles

X(lVlAN.)
miles

Y(MAN.)
miles

DATE 5/9/61

X(V.P.)
miles

Y(V.P.l
miles
+ 45.500

.000

+ 45.375

.125

+ 44.750

.125

+ 44.250

+ 27.125

+ 40.25-0

+ 31. 250

+ 40.500

.125

.000

- 55.250

.250

- 55.250

.375

- 35.375

7.000

+330.375

.125

.000

1.875

+200.000

+ 40.375

.000

+ 40.375

.250

+ 40.500

.125

+ 13.250

- 25.500

+ 12.625

- 25.625

+ 13.000

- 25.875

DIFFERENCES COMPUTED IN RADAR MILES
TRKNO

USM-94 minus STL
DELTA X
DELTA Y

USM-94 minus MANUAL
DELTA X
DELTA Y

.000

18.125

.000

.125

.625

.000

4.000

4.125

.000

.250

+287.125

7.125

.000

.250

.000

.625

.125

+330.375

USM- 94 minus V. P.
DELTA X
DELTA Y
.125

.125

3.750

+ 27.250

5.125

.375

.250

VP REPEATED TARGETS

375
.125
.000
1. 875

+ 45.500
45.500
+ 200.000
+ 200. 000

NTDS CN.
12 sec. search time. and 1 mile subtracted for range compensation on V. P.

Figure 8 - Tracking Accuracy-Calibration of Video Processor and
NTDS

m/s

19.875

.125

.125
+

VP reports within 10 miles of VP
matched targets more than once
X
Y

13.
13.
16.
16.

+130.375

.375

INTEGRATION AND AUTOMATIC FAULT LOCATION TECHKIQUES IN LARGE DIGITAL DATA SYSTEMS

Figure 9 - Memory Chassis Tester

Is waveform. eliminated
when K is set:

PYRAMm DIA.GRAM FOR IDENTIFYING A CIRCUIT
CONTRIBUTING A PECULIAR W:..VEFORM IN A C(J.~POSITE SCOPE DISPLAY
(FOR USE -,-lITH URANUS JI£MORY CHASSIS TESTER)

X: Bits 9,8,7,6,5
Y: Bits 4,3,2,1,0

00-37

ISS
XlXXX

XXXXl

!!.Qll;.: Circuit numbers are octal.
Figure 10 - Pyramid Diagram

223

224

COMPUTER SYSTEMS

AUTOMATIC FAULT LOCATION --- MEMORY TEST
ZEROS
40000 00000
00004 00000
021A JI4B34 EXCHANGE WITH .:::...:.......=-:..
020A JI4E36 EXCHANGE WITH
022B JI4A09 EXCHANGE WITH
CHECK LINE VOLTAGE
ADVANCE INHIBIT CURRENT FOR BIT 5
ZEROS
40000 00000
00!05 00000

021A JI4E34 EXCHANGE WITH JI4133
020A JI4E36 EXCHANGE WITH JI4117
022B JI4A09 EXCHANGE WITH JI4AI9
CHECK LINE VOLTAGE
ADVANCE INHIBIT CURRENT FOR BIT 5
Figure 11 - Memory Test Typeout

COMPUTER MEMORY

CURRENT
TEST

OPERATIONAL

EXECUTIVE
ROUTINE

PROGRAM
.~

~SYSTEM

I
I

DIAGNOSTIC a AFL
STORAGE

..-

PM ROUTINES
(STEAMING WATCH)
------

FAULT LOCATION
REPLACEABLE UNIT
(WHAT ?)

---

CALIBRATION
ROUTINES

FAULT LOCATION
SUB- SYSTEM LEVEL
(WHERE ?)

TEST DATA
---------

PERFORMANCE
I-MONITORING
(IS EVERYTHNG OK]

•
•

---------

OPERATIONAL
PROGRAMS OF
VARIED COMPLEXITIES
FOR DEGRADED
MODES OF OPERATION
I

Figure 2-2 - Proposed Ideal Automatic Fault T..ocation Configuration

225

THE USE OF COMPUTERS IN

ANALYSIS~

Walter J. KarpIus and Ladis D. Kovach
Department of Engineering
University of California
Los Angeles, California

Autonatic COITlFuters, l::ot!". analog and digital,
have attained a prominent place it most modertl
engineering curricula. The comruter is recognized as an important engineering design tool permittirg the student to test tl:e efficacy of a
large numl::er of design hypotheses to determire an
optimum design. In these applications the cor.puter is favored l::ecause it ena1::les the student to
dispense with lal::ori.ous hand cal culations and
because it familiarizes the engineering student
wi th tecclIliques which will subsequently be valuable to him in industry. The application of
automatic computers to anoU.er categorj of engir:.eering courses - courses in metl:ods of analysis is more controversial.
Engineering analysis courses include such
subjects as electric circuit analysis, dynamics,
thermodynamics, fluid mechaniCS, and field theory.
The chief objective of these courses is to instill in tt,e student a rrofound understanding of
fundamental engineering practices and systems and
to give him a constructive insight into the response of engineering systems to varicus excitations. The emrhasis in such courses is on
generalization ratt.er than on specific solution
as in engineering design. Shce autCI:'latic computers can only be used for numerico.l analysis tl:e solution of problems in which all variables
and parameters are specified numerically - it
has been argued that COF.1Futers have little or no
place in courses in engineering analysis. Accordir.g to this line of argument the availability
of a computer enables the student'to "short circuit ll the learning process. Homework and classroom problems in courses in analysis are designed
ideally in such a way that by carl'Jing out the
actual computaticn, the stlldent gahs an insi~ht
into the physical system and obtains benefits far
exceedirg the ir:terpr8tations tb,:t he 1.S a1:le to
draw from the final numerico.l solution. Furthermore, tl:e availability of comruters discourages
the student from a conscientious effort to find
the general and therefore more valuable and elegant solution, rather than a numerical solution
applicable only to a srecific situation. It has
been stat.ed that the availability of analog COtlputers in tl:e late 1940's and early 1950 ' s
greatly slowed the orderly development of the
field of nonlinear control system theory. Most
engineers found it much easier to solve a sfecific problem on a computer rather than to seek
and develop a general theory for handling nonlir.ear system analyses.
At the otl:er extreme are educators who are
so computer-oriented that they recommend tl:at
computers be utilized in ~~ course in engin-

eerir.g analysis at least to some extent. They
argue that although, as yet, tl:e generalizations
which can be drawn from numerical analysis are
limited, this is only a reflection of the relative infancy of the comI=uter field. They feel
that soon a new generation of automatic digital
comI=uters will ce available. These new comruters
will make it possi1::le for an engineering analyst
or scientist to "converse" with the autcmatic
brain, that is, to use the comruter as an extension of his own tl:inking processes. In this way
the use of comput.ers will permit the drawing of
generalizations beyond the scope of the human
mind. Accordingly, it is argued that in order to
prepare the engineering educo.tional field for
this day it is necessary to begin now to reorient
thinking in the direction of computers and computing techniques.
It is not the authors' intent in this paper
to att.empt to resolve these two lines of argument.
Along with most other engineering educators we
recognize the iIEportance of mathematical sophisticaticn and the fostering of the students' interest and acility to make significant generalizations. At the same time we realize that the
computer age is upon us and that no area of
tec[lIlological and scientific endeavor can completely escape its impact. It is the ob~ective
of this paper to demonstrate by means of a number
of specific examples how the utilization of computers can be compatitle with the rasic objectives of courses in engineering analysis. Foremost among these ey.am}les are two categories of
complter uti l i za tion :
1. The arplication of comruters to aid the
student in the visualization of dynamic
or mathematical phenomena.
2. The orening up of new approaches to the
eXI=lan~t.ion of system cehavior - approaches which are out of reach of conventional analytico.l methods.
Monte Carlo Methods and Random Walk Fhenomena
The ano.lysis of fields as they occur in such
engineering disciplines as electrostatics, heat
transfer, and fluid mechanics generally follows
a deductive approach. By applying casic physical
laws such as the law of conservation of mass and
energy and the principle of continuity to a small
rounded region of the field (the differential
element) the tasie partial differential equations
characterizing field rroblems are derived. These
it

This Fu'tlication was sF;onsored t;y· the Educational DeveloFment Frogram, Depirtment of Engineerin&, with financial support from the Ford
Foundation.

226

ANALOG APPLICATIONS AND TECHNIQUES

equEtions include, among others, Laplace's equation, Poisson's equation and the wave equation.
~~thematical techniques such as separation of
variables, conformal transformations, etc. are
then applied to adapt the gen~ral equations to
the two specific boundary and/or initial conditions. This finally results in two mathematical
expressions characterizing the equipotential and
stream lines within the field and specifying
transient variation of the field potential at
specific points. Although this approach is of
unquestioned value and utility both to physicists
and engineers, many students will find an additional alternative approach both interesting and
stimulating.
The second approach is governed b.Y the recognition that the uncertainty principle applies
to any specific particle under the influence of
the potential field. In other words, the classical eauations annly only to the statistical aver~. ~A specific·p~rticle (fluid particle in-a
fluid field, electron in electrodynamics, etc.)
will not follow the stream line which constitutes
the solution to the classical problem, but will
rather describe a "random walk". Accordingly, to
solve a field problem, i.e., determine the potential at some point within the field, ~ this
approach it is necessary to perform a series of
consecutive random walks all commencing from the
same point and to tabulate the results of these
walks.
While this technique will rarely be able to
compete with the more conventional techniques in
terms of efficiency, an important educational
advantage may be gained in familiarizing the student with the field process as it actually occurs
in nature. By permitting the student to compare
the results of classical field problem solutions
with random walk solutions he will gain a deeper
insight into the significance of the mathematics,
that is, generalizations which he draws from a
mathematical analysis will be more meaningful.

A practical method for performing such random walk solutions, originally presented by
Chuang, Kazda, and Windeknechtl will now be described. Analog computing techniques are employed since it is desired to present the data
visually and to facilitate manipulation of system
parameters.

A technique which is well-established in
digital computation involves the use of a sequence of random numbers as computer inputs. By
making a sufficiently large number of computer
runs, and by taking a weighted average. of the
results of these runs, convergence to the desired
solution can be obtained. This technique can be
applied in analog computation b.Y exciting the
computer system with a random noise generator a voltage generator whose output amplitude is
governed by a stochastic expression. The repetitive mode of analog computer operation is useful in performing such calculations because a
large number of separate runs, each with a random

noise input, can be completed within a reasonably
short time.
The boundar,y value problem for which the
Monte Carlo method is applicable belongs to a
family of generalized Dirichlet problems of the
form

where Kl and K2 are arbitrary functions of the i~
dependent variables Xl and x2 re5pectivel~ while
~ and D2 are constants. The boundar,r C is an
arbitrary finite closed curve - a Jordan curve.
The Monte Carlo method provides a solution in the
form of the field potential existing at some
point within the field. It does not provide equipotential curves as do the more conventional analytical and analog simulation techniques.
In principle the Monte Carlo method involves
selecting a point of interest within the field
and from this point commencing a random walk.
That is, a sequence of small steps are taken such
that each step begins at the end of the preceding
step but proceeds in a random direction but always parallel to the two perpendicular coordinate
directions. Eventually each such random walk
will reach a point on the field boundary C. The
potential at this boundary point is recorded and
a new random walk is commenced. Provided that
enough random walks are taken, and provided that
each step in the walk is sufficiently small, it
can be shown that the weighted average of the
boundary intersections will converge to the potential existing at the point in question within
the field.
Referring to Figure 1, assume that the solution of Laplace's equation

is required at some point P inside a region bounded by C upon which the values of ¢ are prescribed.
Starting at P a random walk is taken in which
steps of equal length are made in either a posi~
tive or negative direction parallel to the x- or
y-axis. The walk continues until it reaches C
when it is terminated and the value of ¢ on C,
¢C say, is recorded. This process is repeated
l
n times and it may be shown that
n

¢(P) - limit ~¢c
n--.QO i-l i

(3)

In the computer method to be described, the
random walk is actually performed by the beam of

227

THE USE OF COMPUTERS IN ANALYSIS

a cathode-ray oscilloscope. When this beam contacts the field boundary as defined by a mask
placed over the face of the oscilloscope, the
random walk is terminated and a new one begins.
Some auxiliary circuitry is required to
cause the oscilloscope beam to describe the random walk. It has been shown that when an electrical circuit is subjected to an exciting input
voltage of Gaussian white noise, the response
current of the circuit is a Markov stochastic process and that consequently, the conditional probability density function of the current satisfies
the equations governing random walk phenomena.
For the solution of two-dimensional generalized
Dirichlet problems two independent resistanceinductance circuits with nonlinear resistance are
required. The equations describing the response
of these circuits subjected to two independent
Gaussian white noise sources Fl(t) and F2(t) are

where Xl and X2 are functions of Yl and Y2. The
voltages generated by solving Equations (4) on
the computer are employed to drive the oscilloscope beam in the x and y directions. Accordingly, the solution of a Dirichlet problem of the
type described by Equation (1) takes the following steps:
1. Two resistance-inductance circuits governed
by Equation (4) are simulated. In general
these governing equations will be nonlinear.
2. Two independent voltage sources of white
noise Fl and F2 with adjustable spectraldensity D1 and D2 respectively, are employed
to drive the two resistance-inductance circuits.
3. The voltage outputs Yl and Y2 of the two nonlinear circuits are used to drive the horizontal and vertical inputs respectively of
a cathode-ray oscilloscope. The prescribed
boundary C is introduced in such a way as to
make detectable the impingement of the oscilloscope beam on the boundary.
4. A value of F(Q) must be generated to correspond to any point Q on C on which the beam
makes contact with the boundary.
5. A continuous record of successive generations
of F(Q) must be kept or, alternatively, successive values of F(Q) must be continuously
recorded. In either event the mean value of
all the individual results must be determined.
6. At each occurrence of incidence, the oscilloscope beam must be reset to the initial
point inside the boundary C, the point at
which the solution of Equation (1) is desired and at which each random walk of the
oscilloscope beam must begin.

This cycle of operation must be repeated continuously until such time as the value of the mean
of the summed boundary values F(Q) ceases to
change. A block diagram and some physical detail
of a computer system for the solution of Laplace's
equation
(5)

is shown in Figure 2. In this case the potential
distr~bution along the boundary was such-that C
could be divided into two parts by a straight
line so that the arc length (which is a function
of Xl and x2) of each part was a single-valued
function of the length of the dividing line. In
field problems of heuristic interest it is nearly
always possible to find such a dividing line.
Under these conditions two diode function generators suffice to obtain the value F(Q). The incidence of the beam on either of the two sections
of the boundary is detected by means of one of
two phototubes which trigger a gate. This in
turn permits the output of the two diode function
generators to apply voltages determined by the
boundary point coordinates to the F(Q) register.
By suitable timing circuits, each run can be made
to last from one to 3 seconds. In this manner a
reasonably large number of runs can be completed
in a very few minutes; at the same time the trajectory of the oscilloscope beam during each run
will be clearly visible to the observer. The
opaque mask shown in the figure is opaque only
to the detecting photocells. It transmits sufficient light to enable the observer to see the
movement of the oscilloscope beam quite clearly.
The generation of the variables Yl and Y2 in
Equation (4) is effected by means of a circuit of
the type shown in Figure 2. This circuit requires two analog summers, an analog integrator
and a function generator. Low frequency noise
sources of Gaussian amplitude distributions
having the necessar,y power spectra are commercially available. Such devices generally employ
a ~as tube such as a thyratron as the basic
noise source.
Experiments have shown that good convergence
of the random walk solutions to the analytical
solutions in one- and two-dimensional boundary
value problems are obtained if approximately 300
random walks are carried out.
Other Analytical Techniques
There are a number of other ways in which
computers may be used effectively to bring a
deeper understanding of some phase of analysis.
In f~nding the complex roots of a polynomial
equation6 for example, the method of steepest
descent provides a useful technique. In this
method a related function is minimized in a continuous and automatic manner. If the function

228

ANALOG APPLICATIONS AND TECHNIQUES

A description of the automatic nulling process associated with the method of steepest descent on an analog computer has been recently
described. 2

realm of the nonlinear. Unfortunately this is unexplored territory becau~e the analytical techniques tresently in use are linear in nature.
This is true of such giantE in analysie as the
Laplace transform, the Fourier transform, the
Cauchy residue theorem and others. Attempts to
extend these tools to nonlinear problems have met
with little success.

A simple variation of this method has even
wider application. Once the computer has obtained the root of the polynomial equation by the
nulling process it may be operated in an automatic tracking mode. Thus, i f one or sever.l of
the coefficients of the polynomial are varied,
the computer will follow the root to its new location. This technique is extremely use~~l to control-system engineers who use this root-locus
tracking to obtain information about the stability
of control systems. 2

Thus, for lack of adequate analytical techniques for solving nonlinear problems, the use of
computers becomes mandatory. The c:nalog computer,
in particular, is useful for studying nonlinear
problems. Such studies can help the student
visualize nonlinear system behavior and may even
lead to L~portcnt peneralizations and new analytical methods. Certain modifications of the analog
compute-r are necessary, ho",~ever, in oreer to adapt
it to nonlinear studies. These consist of repetitive operation, automatic programming, and means

has a minimum at only those points where the polynomial equation has roots, then finding the minimum is equivalent to locating a root.

f'n,..
--

Another analytical approach which can be
clarified for the student by the use of computers
is conformal mappiIlf!. Any attempt to map the
z-plane into the w-plane by means of the function
w = fez) must necessarily be done point by point.
With an analog computer, however, a curve in the
z-plane can be continuously mapped into the wplane in a matter of seconds. Tomlinson3 has descrihed the circuitry required to map a circle
into an airfoil shape.
Both the Fourier transform and the inverse
Fourier transform of a function can be obtained
on an analog computer. 4 A by-product of this
method are the Fourier coefficients in the expansion of the function. Thus Fourier analysis can
be done on either a digita15 or an analog computer. Again, the advanta~e of the latter is in
helping to visualize the process and making it
easy to see the result of chan~es in the function
being analyzed.
FinallYJ mention should be made of the work
that Bellmanb has done in dynamic programming.
This technique was developed to solve variational
problems which arise in economic, industrial,
engineering, and biological contexts and for
which the classical calculus of variations methods
are inadequate. By utilizing the capabilities of
the digital computer Bellman has developed a new
technique which has the advantage that it handles
linearities or nonlinearities, constraints or not,
implicit or explicit functionals, in preCisely
the same manner, and with the same basic equation.
Nonlinear Analysis
In this "space age" more attention is being
given to nonlinear analysis. As it becomes increasingly important for mathematical models to
match physical situations more closely, more
thought must be given to topics like nonlinear
differential equations, both ordinary and partial.
As we dispense with incompressible fluies, perfect
gases, isotropic solids, frictionless materials,
weightless bars, etc. we are forced into the

t"h~nC';nC'
_ ... _ ... t::>- .... r::-

t.hp
_ .........

rlPC'l"PP
--t-.'- _.-

nf'
--

nnnlinp~'I"it.,,_
.....
- ..... __ .... _ - - - -e1 ,.

Repetitive operation is well known by now 8S
most modern computers have provisions for it.
Older installations can be easily converted by
the addition of an integrator whose output rCJllp
is used to energize relays which in turn clamp
the integrators in the problem. The repetition
rate is controlled by the rate at which the ramp
is genercted. Care must be exercised so that the
repetition rate is not so bi~h that the problem
frequencies exceed the frequency-response limitations of the amplifiers.
Automatic programming7 consists of changing
problem par~meters by predetermined increments.
This is done by ~enerating a monotonically increasing step function. The circuit for this is
energized by the repetitive reset pulses and is
shown in Figure 3. The step funct.ion generated
can be used in a number of ways in parameter
studies.
One of the most common changes that has to
be made in a problem is changing a potentiometer.
This can be done by applying the output of the
step-function circuit to a multiplier which then
multiplies a variable by a constant. Figure 4
shows the circuit for accomplishing this.
Automatic chan~es in initial conditions can
produce a family of solutions in a short time. A
typical example of this is shown in Figure 5.
The analog computer is basically a device for
solving linear problems. The introduction of
nonlinearities increases the complexity of the
equipment which often results in decreased reliability. It is now possible, however, to represent
a wide range of nonlinearities in a simple manner.
This is done by using Quadratrons,B no~~inear CO~
ponents which supply the square of an input volta~e but which can provide other nonlinearities by
sL~ple changes in the auxiliary circuitry.
Figure 6 shows the basic circuit with the Quadratron denoted by "P""

229

THE USE OF COMPUTERS IN ANALYSIS

The characteristic of the Quadratron is a
result of the silicon carbide varistor it contains. In this type of varistor the current
varies as some pO~ler of the voltage. By combining the varistor with ord~nary linear resistance
it is possible to make th~s power verJ" nearly
two. Current is ideally supplied to the Quadratron by an oper~tional amplifier. Thus the
Quadratron-amplifier combination of Figure 6
forms the basic circuit.
The basic circuit is useful, for example, in
representing square-law damping in a mechanical
system. Note especially that the symmetry about
the origin of the circuit's transfer function is
exactly what is required in this type of simulation. There has been a tendency in the past on
the part of some educators to feel that they
have reached a high level of sophistication when
they introduce their clesses to second-order differential equations containing square-law damping.
We can, however, study a large number of systems
each having a different degree of damping quite
easily.
Consider the nonlinear differential equation
m ~ + ,... in( sgn x) + k x .. f( t)
·~(O)

= i(o) ..

The signum function, sgn

.
sgn x ..

- 01 if

if
{

Fi~re

(6)
0

is defined by

x< 0

x. 0

+lif:l.:>O

7 shows the circuit for obtaining

xn(sgn x) for i ~ n S 2. The change in the exponent n is accomplished by means of the potentiometer in the circuit. Solutions to Equation (6)
are obtained by combining a number of auxiliary
circuits as shown in Figure 8.
Some of the advantages of stuQying a nonlinear differential equation in this manner are as
follows:
1. The student is made to realize that the
linear case is a special case -- it is ~ case
out of an infinite number of nonlinear cases.
This helps to present linear and nonlinear problems in the proper perspective.
2. Tne student obtains an idea of how much
the exponent can differ from unity before the results change appreciably from the linear case.
This gives him a feel for the amount of linearization that can be applied to a given problem.
3. The student can examine the family of
output curves and relate the changes to the
changes in the exponent. He m~ thus be able to
generalize the results.
4. The student becomes familiar with nonlinear systems in general through the visual presentation from the analog computer. This point is
discussed later in connection with limit cycles.

More complex equations may be studied by an
extension of the methods described. In this way
greater insight can be gained into the nonlinear
realm which so far has not yielded to general
analytical techniques.
A classical nonlinear differential equation
that has been Widely studied is the van der Pol
equation, usually written
( 8)

This equEltion describes an OSCillatory system
having variable damping. The damping depends not
only on the displacement but also on the parameter E. Different types of solutions are obtained depending on the magnitude of ~ in COMparison with unity. It is a simple matter to
solve Equation (8) on an analog computer with the
techniques already described.9
One of the most important features of the
study of nonlinear differential equations on an
analog computer is the insight it gives the student into limit cycles. These are closed curves
representing a steady-state periodic oscillation
determined only by the characteristics of the
equation itself, and independent of the way the
oscillation is started. If the initial point is
inside the limit cycle, the solution curve will
spiral outward until it reaches the limit cycle.
If the initial point is outside, the solution
curve spirals inward. It would be too timeconsuming to see this phenomena if the solution
curve had to be obtained and plotted point by
point.
Network TOpology
Since 1954 much work has been done in the
study of electrical networks from a topological
viewpoint. Any network diagram represents two
independent aspects of an electrical network: the
interconnection between components and the voltage-current relationships of each component. Network topology is concerned with the former aspect.
Essential to this type of ar~ysis is graph theory,
a fairly recent branch of algebra.
These new techniques have led to the synthesis of conventional electrical networks and
combinational switching networks by algebraic
methods. When the network h85 8 large wlmber Qf
vertices (or nodes), however, the computational
work becomes prohibitive and the use of a computer becomes mandatory.
The analysis and synthesis of electrical
networks by topological methods with a digital
computer has been described by various authors.
One of the first of these was Van Valkenburg. lO
More recently Watanabe ll has given a computer
method for finding all possible trees and/or
multitrees in a network.

ANALOG APPLICATIONS AND TECHNIQUES

230

With the advent of parametric amplifiers
there has been a renewed interest in the analysis
of networks containing periodic parameters. When
even one periodic circuit element is introduced
in a lumped, linear, finite, passive, bilateral,
time-invariant network, the analysis of the resulting network becomes a formidable task. Leon
and Bean12 have shown how a digital computer may
be useful in this case.

Conclusion
5.
Automatic computers have a definite place in
engineering analysis. Analog computers, in particular, are useful in helping the engineer
visualize dyr~~ic phenomer~ and in giving him a
feel for the effect that various parameters have
on the solution& The use of automatic programming techniques are helpful in making generalizations which may be impossible to achieye without
the time-saving feature of the computer.
While the use of computers in design may be
important to the engineer (espeCially from an
economic standpoint), the real contribution of
the computer will come from its use in analysis.
With the assistance provided by the computer the
analyst can make significant progress in extending man's knowledge of his environment.

9.
10.

References
1.

11.

Chuang, K., L.S. Kazda, and T. Windeknecht'
A Stochastic Method of Solving Partial Differential Equations Using An Electronic
Analog Computer, Project Michigan Report
2900-91-T, Willow Run Labs., Ann Arbor, Michigan, June 1960.

A random walk in the

Mo~te

Carlo method

12.

Kovach, L. D. and H. F. MeissingerJ Solution
of Algebraic Equations, Linear Programming,
and Parameter Optimization, Part 5.11 of
Computer Handbook edited by Huskey and Korn,
McGraw-Hill Book Co., Inc., New York, 1962.
Tomlinson, N.P., et all Analog-computer Construction of Conformal Maps in Fluid Dynamics, J. Appl. Phys., 21:307 (1950).
Kovach, L.D.: Miscellaneous Techniques, part
6.6 of Computer Handbook edited by Huskey
and Korn, McGraw-Hill Book Co., Inc., New
York, 1962.
Szymanski, E.: Analysis of Non-Sinusoidal
Voltage Wave-Forms, article in Electronic
Computers in Engineering Education, Univ. of
Mich., Aug. 26, 1960.
BelL'Tlan, R&! Some New Techniques in the Dynamic Programming Solution of Variational
Problems, Quart. Apple Math.,vol. 16, pp. 295305, 1958.
Douglas Aircraft Co~ Report E~S~ 40427: Automatic Analog Mechanization of the Shock
Spectrum Problem, Aug. 18, 1961.
Kovach, L.D. and W. Comley: A New, SolidState, Nonlinear Analog Component, IRE Trans.
on Elec. Comp., vol. EC-9, no. 4, pp. 496=
503, Dec., 1960.
Kovach, L.D. and W. Comley: Simple Analogs
for Useful Nonlinearities, Cont. Eng. 7(11),
Nov. 1960, 135-137.
Van Valkenburg, M.E.: Topological Synthesis,
IRE Wescon Record (part 2) 2,3-9, (1958).
Watanabe, H.: A Method of Tree Expansion in
Network Topology, IRE Trans. on Circ. Theo~,
vol. CT-8(1), 4-10, March, 1961.
Leon, B.J. and G.A. Bean: Analysis and Design
of Parametric Amplifiers with the Aid of a
709 Computer, IRE Trans. on Circ. Theory,
vol. CT-9(3), 210-215, Sept., 1961.

231

TlIE USE OF COMPUTERS IN ANALYSIS

OPAQUE / /

MASK

DIVIDER

I
TRIGGER

OSCILLOSCOPE

.-/7~:::'- x:;;...,T ¥-'.'UT

>~//
~

OTO-TUBES

~----+-----4 ~(t)

~-----+-..... y,Jt)
co.

TRIGGER
DIODE
FUNCTION
GENERATOR

DIODE
FUNCTION
GENERATOR
(0)

NOISE
F, (t)
GENERATOR

~(t)

~ (y,j FUNCTION
(b)
2.

Solving Laplace's equation by the Monte Carlo method (after Chuang, et all)
a) Block diagram of system
b) Circuit for generating random walks

232

ANALOG APPLICATIONS AND TECHNIQUES

SOLUTION
START SWiTOH

t
r--1

r lI II

RESET
PULSE

-E VOLTS
3.

Step-function generator

MULTIPLIER
INPUT

Ell

OUTPUT

STEP
FUNOTION

E·L

t
4.

Automatic changing of a constant coefficient

THE USE OF COMPUTERS IN ANALYSIS

233

4~ dt+ I.C.

ledt
o

INPUT
e o----t

~----o

OUTPUT

I.C.
Tn
~TC'D ,_,
~IIN~TlnN
. _ v....
.. v, 'v ... t.!C'NC'DATnR
v ...... , .... v ,

FOR INITIAL CONDITION

TYPICAL
PROBLEM
VARIABLE
} VALUES OF I.C.

t
,.

Automatic changing of initial conditions and the resulting solutions

S.J.
INPUT

4
Do----......
el

.a.",..oo----.g

Basic circuit and transfer function of the Quadratron

ANALOG APPLICATIONS AND TECHNIQUES

234

o---,\A/VVV+t.ft-. . .-4

INPUT

el-K.. (sgn el)

~ sns

e.=- Kent (sgn Ii',

I , in the physical problem. In the alternate arrangement the surface is energized along
boundaries that are the direct analogs of two
stream lines in the physical problem. The latter
approach was adopted in this investigation. This
flexibility is due to the orthogonality of the fluid
l"": __ _ _
f10\1:/ potential lines and stream lin.es.
uU1C t:: In LIlt::
actual physical problem, the components of gas
velocity u and v are related to the gas potential
and stream functions cj> and cj>' by the previously
mentioned Cauchy-Riemann conditions, it follows
that in this simulation
~

..I.

_aV(x,y)
u (x, y ) ay

(5)

aV(x, y)
_
v (x, y ) - ax

(6)

where V (x, y) is the conducting surface voltage at
the point (x, y).

Finite difference approximations to these partial derivatives can be obtained by using a multipronged probe which measures the potential at
several points in the vicinity of (x, y). As an example of one possible arrangement, consider that
indicated in Figure 1. The symmetrical probe
consists of four Jlpoints II

®~

--~-~----;t---'-

-r- ."

b.y

+'J---t---..,-

Figure l.

Orientation of Four- Element Probe

which measure respectively the voltages 4; 1, 4;2,
4; 3' and 4; 4 near (x, y). The following relations can
then be written
a4;
ax

a4;
ay

4;2 - 4;1 + 4;3 - 4;4
4f::..x

(7)

4;1 -4;4+4;2-4;3
4f::..y

(8)

The determination of voltage derivatives by averaging two finite voltage differences in this way
(instead of using only one difference) has certain
advantages which will be discus sed later.
In view of Equations (5) to (8) it is apparent
that the driving voltages for the analog computer
mechanication can be obtained directly from 4; 1 to
4;4 taking into account proper polarities and certain constant scale factors. Figure 3 schematically
indicates the required signal flow lines.
C.

Sources of Simulation Errors

Let us now give a brief qualitative description
of the major sources of simulation errors. A
quantitative discussion of the errors appears in
Appendix B. These errors can be conveniently
broken down into conducting surface errors, probe
errors, and analog computer component errors.
It is as sumed that the X- Y plotter, upon which the
conductive surface analog is carefully oriented,
can be adjusted to have sufficient sensitivity and
that the effects of plotter backlash can be minimized.
1.
Computer Errors. Servo Multiplier
Errors. Since servos are used to perform the
required multiplications, the effects of misalignment of the various servo potentiometers must be
considered. Other servo error sources will be
assumed negligible.

ANALOG APPLICATIONS AND TECHNIQUES

238

Probe Element Gain Errors. If each
probe element is not multiplied by precisely the
same computer gain, significant errors in the
simulated particle traj ectory will result.
Other computer errors v.lill be assuITled
to have negligible effect on the simulated particle
trajectories although it should be pointed out that
it is extremely important to accurately balance
each amplifier to have zero output for a grounded
input.

2.
Conducting Surface Errors. Misalignment of the conducting surface coordinates with
respect to the coordinate axes of the X- Y plotter.

a particular problem since it takes no account of
the potential flow field's geometry. To illustrate
this point consider a specific value of error, Or,
at both xl and x2 at which the cross-sectional
dimensions are respectively AA and BB. Now or
is apt to be far more critical in the latter case
and thus, perhaps, or should be weighted by some
geometrical surface dimension. No dimension
stands out as the obvious choice. The one selected
here is the distance, D, between boundaries normal to the particle velocity vector. A typical D
is illustrated in Figure 2. Thus the error criterion becomes

Nonhomogeneity of the conducting surface
resisti vity.
Computer loading effects on the conducting surfae e.
3.
Probe Errors. Errors caused by
approximating surface voltage derivatives by the
differences of finite surface voltages.
Angular misorientation of the probe on
the carriage of the X- Y plotter.

This is probably the most useful criterion
since it deals with a weighted error magnitude.
Ho'",ever, E (t) constantly changes with time and is
thus only a local figure of merit rather than a
figure of merit for the entire traj ectory. To
establish such a criterion for the entire trajectory
the weighted rms trajectory E is adopted.

Probe elements becoming dirty or
jammed in their housing causing nonrepeatable
solutions.

III.
A.

E =[~
(t)

1
r

11/2

(13 )

Error Analysis

Error Criteria

The errors mentioned in Section II-C will
cause errors in the x and y components of the
particle trajectory. As will be shown subsequently, a quantitative measure of this error in
a given particle traj ectory can be obtained from
a suitable error model having the aforementioned
errors as lIinputs." However, even when the
errors in a given particle trajectory can be determined it is necessary to be able to evaluate the
tolerability of these trajectory errors by some
standard criterion.
Irl. order to illustrate the difficulty'" a.ssociated
with a comparison of trajectories by an error
criterion in problems of this type consider the
exact and actual trajectories in Figure 2. At a
specific value of time, say t', the coordinates of
the exact trajectory are x(t'} and y{t') whereas
the actual simulated trajectory has coordinates
x' (t'), y' (t'). Therefore the coordinate errors are
ox(t'}

= x' (t')

- x(t'}

(9)

oy(t')

= y'(t')

- y(t'}

(10)

and the magnitude of the traj ectory error is

or(t')

(12)

D(t)

2l 1 /2

= Lox(t i )2 + iSYl"f1T j

(11 )

While or (tl) is the actual trajectory error, it
alone may not be a sufficient criterion for evaluating the usefulness of this analog simulation for

Equations (12) and (13) represent useful error
criteria. However, the "nature of the error equations (whose derivation follows) causes E and E to
be extremely sensitive to trajectory length Ir dr
due to the double integrations of particle accelerations (in which the error sources occur) in the
determination of ox and oy. Thus the expected
traj ectory error at x2 exceeds that at xl' for
example. While E and E are not necessarily
linearly related to Ir dr, a more useful set of
criteria for comparing simulations of this type is

r.~x 2 + oy 2l1/21~
1 l-l
J
~ r
d

(14)

The example considered in part C of this section
specifies trajectory errors in terms of E rand Er .
It is, of course, an easy matter to convert back
to E and e.
B.

General Trajectory Equations

The previous section was devoted to qualitative aspects of error in a particle trajectory. It
is the intent of this section to derive a mathematical model that will adequately characterize the
behavior of this error in a quantitative fashion
once the inputs to the error model have been
specified. The structure for deriving the error
model is indicated schematically in Figure 3.

ANALOG SIMULATION OF PARTICLE TRAJECTORIES IN FLUID FLOW

239

v-v + oV

The pertinent equations are easily derived from
the basic system equations, namely

+ E ZZ

(30)

(31)

..
s
x = RWx

(horizontal particle
acceleration)

(16)
(3Z)

..
s
y =-w
K
y

(vertical particle
acceleration)

Z
s = s (w )

(17)

(18)

wZ = w Z + w Z
x
y

(relati ve velocity
squared)

These values replace the original terms in Equations (16) to (ZZ). 6w Z, ou, oV, 6s are replaced
in the resultant equations by noting that*
6w

(19)

= 6 (w Z + w Z) = Zw 6w + Zw 6w
y
x
x
y
y

6u = V
(gas velocity relations
in terms of surface
voltage deri vati ves)

+ V yy

= 0

(Lap lac e I s equation)

(34)

6v = -V

6x - V

(3S)

(Zl)
os =~owZ
Z
dw

(ZZ)

(Z3)

- x

6x + V

(ZO)

Here (x, y) are the particle coordinates, u and v
the corresponding components of gas velocity at
(x, y) and Wx and Wy are defined by
w

(33)

(36)

This leads to two lengthy equations in
+
and
oy, which, upon subtracting respectively
Equations (16) and (17), yield the desired differential equations

V+

Z
[d
d
Ll dl +a Z dt

+a~ oX +L 4 dt +a~oY=El

(37)

(Z4)
(38)
These equations are mechanized on the analog
computer to yield the particle trajectory coordinates (x, y) as continuous functions of time. However, the independent additive errors discussed
in Section II-C and indicated in Figure 3, namely
oVx ' 6V y ' Ef, Ell, E lZ, E Zl, and E ZZ, give rise
to trajectory errors 6x and oy and hence rise to
gas velocity error s 6u and ov due to mispositioning of the X - Y plotte r. Thus, ins tead of solving
the desired Equations (16) to (ZZ), the computer
solves these equations with the dependent variables
replaced by the following terms
u---u + 6u + oV
v __ v + ov -

oVx

(ZS)

(39)

b
+ ox

(Z7)

'1-'1

0'1

(Z8)

+ ox + E

(Z9)

In this section an alphabetic subscript
denotes a partial derivative with
respect to the subscripted variable.

= s + Z ~wZ
Z
dw

(40)

(41)

3 = -

(26)

x-x
x-x
*V = ov
x
ox'

where

=[s

+Z~wZ-!V
J
dwZ

*All

= b

(4Z)

ds
Z--ZwwV
dw
x Y xx

(43)

dwZ

Y yy

Z~w w
dwZ

"'"'I

z~wZlv
dwZ

Z~w w V

2~w2JV
dwZ y
xy
a

(44)

Z~w w V
dwZ

Y xy

(4S)

items greater than first order are neglected.

ANALOG APPLICATIONS AND TECHNIQUES

240

Z~w w V
dwZ

r
'C"'
.1.:..1
-- K'
... " lZ ..L' II ~
l

0:>

E2 = K, 22 -

..L

....

[S +

il
I

ds
-Z ""
.. x
dw_

2 ::2

Z dS wxw .. oV ..
dwZ
Y
Y

Y yx

(46)

F. \T

~'y

WY~ 6V

+ W ••
Y

ds Z (E ... + El l~
Z
llef + dw
......J
1

(48)

The ai and bi above are time varying coefficients available from the simulation. El and EZ,
the inputs to Equations (37} and (38), are generated by the error sources oVx' oVy ' Ei' Ef and
certain other obtainable time varyIng coefficients
as indicated in Equations (47) and (48). oVx and
oV y are the accumulation of errors inherent in the
analog determination of u and v.

negligible and thus a more optimistic answer will
result than if a more complex problem had been
considered. Nevertheless, this example should
lend a deep insight into the more general problems and permit the use of engineering judgment
to predict errors for more complex cases. Also
the results of this example establish a lower
limit on expected trajectory errors for a problem
more involved than this one. The flow field configuration and trajectory chosen for this example
are indicated in Figure 4 which represents the
conducting surface analog of the fluid flow field.
A voltage difference of Vs is applied across two
parallel boundaries of the field as indicated in
Figure 4. The particle (represented by the probe)
begins at point A (x = 0, y = Yo) with the same
velocity as the fluid U, and follows trajectory
A-C up to some final point. This trajectory differs from the ideal trajectory A-B due to errors
in the simulation. The object is to determine the
magnitude of these errors and weigh them by the
aforementioned criteria. For this case, Equations (37) and (3 8), the error model equations,
simplify to
Z
d
K-ox
Z
dt

;

K-6y
dl

~ox
= El
dt

d
s dt 6y

(51)

(5Z)

where K and s are constants and
where
refers to voltage error sources caused
by conducting surface misalignment
refers to voltage error sources caused
by angular misalignment of probe

(53)

refers to voltage error sources caused
by unequal probe element gains
refers to voltage error sources caused
by finite difference approximation to

voltage gradient components
refers to voltage error sources caused
by conducting surface irregularities
Ell' E lZ' E Zl' E ZZ are errors sources
caused by inaccuracies in the computer servo
multipliers and Ef refers to errors in the function
generator. A detailed discussion relating these
voltage error sources to their physical causes is
presented in Appendix B.
C.

Example

The preceding error analysis is now applied
to the simple problem of determining the particle
traj ectory error in a fluid flow field characterized
by parallel stream lines. This problem is considered since the error equations simplify to the
extent of permitting a solution without the use of
elaborate computing equipment. One shortcoming
of this example is that many of the errors become

(54)

A derivation of the above expressions for El and
EZ is included as Appendix C.
All other terms in the general error equations can be neglected since they involve either
products of small terms such as w x ' w y , E lZ,
etc., and thus introduce only second order effects
or because they involve V xx ' V yy , V XY ' and
ds/d(w Z) which are zero for this problem. The
vanishing of the second order partials of surface
voltage is a characteristic of parallel stream
lines; ds /d(wZ) equals zero, since for low
Reynolds Numbers s is approximately constant,
this constant being unity.
To evaluate the error of the trajectory let the
error indices defined by Equations (14) and (15)
be computed for this example (where D is unity).

241

ANALOG SIMULATION OF PARTICLE TRAJECTORIES IN FLUID FLOW
A

x+8x
y+8y

\
\

1a=1

',-,I

x-v

SOURCES OF ERROR

PLOTTER -Vs/2

8V AND 8Vy
X

Figure 3.

Simulation Schematic

RDER

/ Vs/2

-----------____
----c

A--------------~_~~---_-

/
/
/
/
/
/
/
/
/
L
y

I / / I I / /

:=0

Figure 4.

-Vs/2

yt:

A Particle Trajectory in a Potential Flow
Field with Parallel Stream Lines

ANALOG APPLICATIONS AND TECHNIQUES

242

er
r =

!r!
rlr
L

Or
r

(55)

(or)

~ I/Z

(56)

..J

where oXI is the solution of (51) when EI is replaced by fI' oxZ is the solution of (51) when El
is replaced by g l' 0Yl is the solution of (5Z) when
EZ is replaced by fZ' and oyz is the solution of
(5Z) when EZ is replaced by gz'
Consider now the evaluation of (or) Z and

(dr) Z = (dx) Z

where

(dy) Z

(57)

and where

= l/t f ot (6r) Z dt.

(or)Z
(or)

= (ox)

(oy)

(58)

80Xl)Z

(60)
where

(OYI)~

+ Z ~xloxZ + OYI0Y~ + ~OXz)Z + (Oyz)Z]

Observing Equations (53) and (54) it is noted
that all terms except 05Vx and 05Vy remain constant for the duration of a trajectory run. It
therefore becomes convenient to reduce El and
EZ to the following forms:
(59)

_ rt

t f ~OXz)Z + (OYz)~

(oxlox Z

oy lOy Z) dt'

dt'

It is apparent that once (or) Z and oZr have been

(~y)(v:)

(G Zy - G 4y)

determined, the chosen criteria Er and Er defined
in Equations (55) and (56) respectively follow
immediately

(4~Y)~~) + 21 IZ

(61 )

(6Z)

£Z

(G 3x - G 1x)

(G Zx - G

(4~X)~J

4x)(4L)(~) +

ZlZZ

(63)

Unfortunately (or) Z cannot be computed unles s
oxZ and oYz are first determined as functions of
time. However, this involves complete knowledge of the conducting surface characteristics as
a random function of x and y which is difficult to
obtain. Therefore the best that can be done in
evaluating (or) Z is to determine the effects of all
errors except those originating from the conducting surface. To this end define

(64)

In Equations (59) and (60), f 1 and fZ will as sume
some constant value throughout the determination
of a given trajectory whereas gl and gZ will each
be a two-parameter family of random variables
with the coordinates x and y as parameters. Since
Equations (51) and (5Z) are linear, the total solutions ox and oy can be decomposed as follows

(69)
Since fl and fZ are constant throughout the
determination of anyone trajectory, (oxI)Z and
(oYl) Z are easily determined by solving Equations
(51) and (5Z); the results, for zero initial conditions and s = 1, are:

(OX1)Z

£/ {t -KQ_ (-t/KB} Z

(65)

(OYI)2 = £Z2
(66)

(68)

*
(G 1y - G 3y)

(67)

U = 1 for this simple problem.

exp

{t -KU-

exp

(-t/KB} Z

(70)

(71)

The relationship between time t and trajectory
length r for the trajectory shown in Figure 4 can
easily be obtained by integrating the equations of
exact particle motion: x = y = 0 subject to

ANALOG SIMULATION OF PARTICLE TRAJECTORIES IN FLUID FLOW

x(o) = 1, y(o) = 0, x(o) = 0, and y(o) = Yo' The
result for this trajectory is that r = x = t. Substituting this result in Equations (70) and (71)
enables Or', defined by Equation (69), to be evaluated as

243

--L..}L
G
- G
3x 4.6.x V
/ Ix
s

(72)

0.0025

(78)

where
(73)

and

(74)

Although it is known that f 1 and f2 (and thus
f3) are constant for the entire run, it is. not known
with certainty what value the constant WIll as sume.
At best, one can only assume probability density
functions for each of the individual terms of fl and
f2 ~ee Equation (61) and (63~ and then the density
functions for fl' f2' and f3 follow. Each of the
individual terms in fl and f2 will be assumed to
possess a uniform probability density as sketched
in Figure 5.

Implied in Equation (78) is (Y /4.6.y) = (Y /4.6.x) =50
which corresponds to the value used in actual simulations; and V/Vs = O. 5. The probability density
function for f 1 and f2 can be determined by convolution of the density functions of the terms that
compose them. Given the density functions for fl
and f 2 • the density function for f3 follo.ws. T~e
details are given in Reference 23. Thls functlOn
is presented in Figure 6 where the abscissa values
correspond directly to values of f3. By Equation
(72), the probability density function for E~,
pI
(z) versus z, can be obtained from the same
fiEg~re by noting that f3 = zQl-l (K/x). Thus a
rather complete picture of E r is obtained for the
effects of all errors except the random conducting
surface irregularities.
Consider now the evaluation of o2r in Equation (68). Since f 1 and f2 are constant, the first
integral can be solved using Equations (70) and
(71); reali zing that r = t yields

p(z)

ii
(79)
where
h

Figure 5.

(80)

Uniform Probability Density Function

The maximum limits of each of the terms in
fl and f2 must now be discussed. The limits
as sumed are

lal:::: O. 00312

rad

1131 :::: O. 5 degree = 0.0087 rad

(75)

(76)

Equation (79) is of the same form as Equation (72)
and thus Figure 6 can be used to predict the rms
traj ectory errors due to all causes except surface
noise.
The last integral in Equation (68) can be
broken into two parts. Considering the first part,
namely

(77)
it follows that by the convolution integral

(81)

ANALOG APPLICATIONS AND TECHNIQUES

244

where h(t) is the impulse response of the linear
system defined by Equation (51). Thus it follows
that

An average autocorrelation function was experimentally determined by averaging the results of
several trajectories and found to be of the form

(85)

where" is a surface distance argument in the x
direction measured in inches. Converting 1)., to a
time argument [as required by Equation (84)J
Equations (85) and (84) can be solved to yield
interchanging order of integration yields:
-ZZ
(t
(t
t
( (0 _) dt' = f dThlT) I dc.rhlc.r)

.!.
t J0

,xL'

) 0

•. ) 0

{)

T) g, (t' - c.r)
-.1

dt~J

ZKx x

z = -Cx

~Kx K3 ~ x

KKlf

-~)

+_x_~_eK
Z Z
~x
K ~
- 1
L
x
.J

(8Z)

The bracketed term is a psuedo autocorrelation
function of random surface irregularities.
This
function can be experimentally determined for a
gi ven straight line traj ectory on a given conducting
surface. Considering a different straight line
trajectory displaced somewhat from the first generally results in an autocorrelation function of
surface irregularities that is different from the
original.

r~ - e -ZR)

These considerations make it most reasonab~__!..o compute the expected value of oZr, namely,
E(oZr). From Equations (68), (79), and (82) the
result will follow.

(86)

(83)

where
~

E(f}) can be obtained simply by taking the second
statistical moment using the distribution function
in Figure 6. The second term in Equation (83)
vanishes since oXl, OY1, oxZ, and 0YZ are all uncorrelated and assumed to have zero mean values.
The evaluation of the first integral of the third
term can be obtained directly from Equation (8Z)

= I0t dTh(T)

I0t dc.rh(c.r) t1

Y {,,)=K

-k

I" I
~

/"'t

. Jo Egl(t' - c.r)gl(t

i
-

c.r)de (84)

A detailed treatment of these concepts may be
*found
in Reference Z5.

= k L'

(87)

An identically similar result follows for the evaluation of oZyZ except that Ky replaces Kx and ~y
replaces ~x where

1o
Jt
t
E (ox) Z dt

1.7xlO- 4 e-1.

= k L'

4Z I
"

(88)

(89)

245

ANALOG SIMULATION OF PARTICLE TRAJECTORIES IN FLUID FLOW

All the error sources have now been considered
in the evaluation of o2r. The total expected mean
squared error is then obtained using Equation (83).
The square root of this equation divided by r yields
~ r.
The results are summarized in Table 1 below.
Table 1.
Expected
Total
rms
Error

Surface
Noise
Errors

Expected Fixed
Trajectory
Errors
Caused by f ,f
1 2

or/r

Or /r

or/r

or /r

1/10

5 in

0.0114

0.0033

0.0059

0.0119

1/10

10 in

0.0083

0.0033

0.0059

0.0089

4/5

5 in

0.0058

0.0014

0.0028

0.0060

4/5

10 in

0.0042

0.0014 0.0028

0.0044

K/r

Note: r

in all cases.

Note that errors increase with an increase in
the K/r factor and decrease with an increase' in
L'. Thus inertia parameter K of 0.5, corresponding to a characteristic dimension L that reflects
to an L' of 5 inches in the simulation, will result
in 1. 19 percent normalized rms trajectory error
for the conditions assumed in this example. The
above table also contains the expected trajectory
error due to the fixed errors fl and f2 considered
in the first part of this example. The surface
noise rms error is also indicated. It should be
noted that errors several times the expected
values are possible but not very likely.
IV.

Simulation Example

Of the many different configurations for which
particle trajector~ simulations were performed
by the authors 22 , 3 one was that of determining
the particle trajectories in an infinite potential
flo~ field distorted by the presence of a cylinder
~Figure. 7). This particular problem is interes!ing
In that It has been solved differently by others -'1=16
and thus pro.vides a good test case for comparing
results obtamed by the technique described in this
paper. Trajectories were obtained using the same
values of inertia parameter K and free stream
Reynolds number Reo ** employed in Reference 16.
The conductinQ' surface used in the n1"nhlprn
is illustrated in Figure 7. By impo~i~g L;~it~g-~-s
along two stream lines a field of infinite extent is

*The

technique used by the authors in Reference
16 was to first obtain a closed form analytic
solution for Laplace's equation and then use this
result in formulating the nonlinear equations
governing particle motion which were subsequently solved on the analog computer.

simulated. A-A' represents a typical particle
trajectory which at coordinates (-5L', yL') has
the same velocity as the gas. The results of the
simulation are shown in Figure 7 (K = 4, Reo
= 6.3. 25) and ~igure 8 (K = O. 5, Reo = 70. 75) in
whlch the ordlnate scale has been expanded to
twice that of the abscissa. The corresponding
solutions of Reference 16 are also plotted for
compa-:t'isbri, and -are comparable but riofTdEmtical
to those obtained using the conducting surface to
simulate Laplace's equation and a multipronged
probe to obtain a. finite difference approximation
to the components of the potential gradient.
If the solutions of Reference 16 are accepted*
as ideal, it is still not possible to determine the
traj ectory errors Ox and Oy in the conducting surface simulation directly from Figures 8 and 9,
since corresponding points at various instants of
time t on the two trajectories are not known. In
order to get a qualitative error measure it is
assumed that Ox and oy are approximately equal,
in which case the errors appear to be about one to
two percent of the trajectory lengths. This seems
consistent with the results obtained with the
simple problem considered in Section III-C.

Since each of the trajectories in Figures 8
and 9 seem to be in error by about the same
amount it is probable that the conducting surface
irregularities (which generally vary with position)
are not the prime source. A prime suspect is a
possible probe angular misalignment since a misalignment of one degree or so would be sufficient
to cause the observed errors.
V.

Conclusions

Based on the results obtained in the error
analysis of particle trajectories in a parallel flow
field and on experimental results of trajectories
in the vicinity of a cylinder it can be concluded
that conductive surface analogs, used in conjunction with an analog computer, can provide answers
that are sufficiently accurate for a wide variety
of problems. It is hard to specify a confidence
level for results in the general case since this is
so dependent upon the shape and size of the conducting -surface, Reynolds number Reo' the traj ectory length r, and the particle inertia parameter K. One can merely apply judgment based on
the results obtained to predict errors in the general case. Let us review these results and
attempt such a judgment.
The error magnitude decreases with an increase in inertia parameter K and increases with
an increase in trajectory length r. For the case
of a particle trajectory in a flow field with parallel stream lines, the trajectory error is solely
a function of K/r once the error sources and
initial particle position have been specified. The
worst case considered in this investigation considered a value of K/r = O. 1 and V/V = 0.5. For
this case the maximum rms trajecto~y error due
to all effects is about 3.5 percent of the trajectory

This i.s identical to Re except that the velocity
term In the equation defining Reynolds number
is replaced by the free stream velocity U.

*This

assumption has not been verified.

246

length with an "expected ll error of about 1. 2 percent. The error magnitude at a particular point
on the trajectory cannot be computed directly
since the effect at a specific point due to conducting surface irregularities is not known. If the
conducting surface error has a mean value close
to zero (which is often the case), then the expected
error at any point for which K/r = O. 1 is about
1/2 to 1 percent of the trajectory length. Higher
values of K/r would, of course, result in lower
error values. In the experimental data obtained
in simulating conditions of flow in a field distorted by a cylinder, the particle trajectory error
in the vicinity of the cylinderls surface was
assumed to be about 1 to 2 percent of the trajectory length as described previously.
Extrapolating the above remarks to the general case, it seems probable that for K/r values
greater than O. 1, the expected trajectory errors
should be less than 2 to 3 percent with errors of
as much as 5 percent possible, but unlikely. It
is obvious that if greater care is taken to reduce
the error sources, the trajectory accuracy will
improve. There is a limit to which this can be
done and as this limit is approached the simulation becomes so sensitive that it loses its basic
advantages and makes other means of solving the
problem more attractive.
Future efforts to improve the accuracy of
this method of analog simulation should be
directed toward the development of a more homogeneous conducting surface than Teledeltos paper;
and toward the construction of voltage sensing
probes that are simple, reliable, aligned properly,
and which accurately form the components of voltage gradient that are required. It would be desirable to determine what sort of tests should be
performed on the conducting surface in the lias
received" condition in order to estimate what its
traj ectory error effects will be once it is shaped
to simulate the required potential field.
Aside from the mechanical design problems
of probe construction, some effort might be
directed towards determining an optimum probe
configuration employing, perhaps, the use of more
than four elements. The ideal or "optimum"
probe element spacing is also an unknown and will
depend on the surface noise characteristics and
the problem simulated. It is pos sible that different probes should be used for different classes of
problems.
Regarding the estimation and analysis of
errors in particle trajectories, it might be desirable to formulate different IIfigures of merit"
or error criteria than those advanced in this
paper in order to get a more meaningful characterization of the error in a given problem.

ANALOG APPLICATIONS AND TECHNIQUES

and provides the investigator with a deep insight
to the physical problem that would not ordinarily
be obtained in as simple a fashion by other means.
In cases where the accuracy is insufficient as
determined perhaps by an error analysis, a more
sophisticated method of solving the problem might
be preferable; the use of a digital computer might
be an alternate means in this case.
Appendix A
Derivation of Mathematical Model
This appendix will present a brief derivation
of the mathematical model used in the simulation.
The eight as sumptions cited in Section II are
assumed to hold throughout the derivation.
The motion of a particle in fluid flow is
governed by the conventional equation for the drag
force of a body in a fluid. Throughout the analysis,
particles will be assumed to be spherical in shape.
From the definition of drag coefficient CD' the only force acting on the particle is

F = -1 P 'ITa 2 C I~
Wi
2 g
D

(A-l)

where a is the radius of the particle, Pg is the
density of the gas, and Wi is the relative velocity
between the gas and particle, viz*

=lGI (Xl, yl) -

~ 1/2
x~2 + ~I (Xl, yl) - y~2J

(A-2)

where u l (Xl, yl) and Vi (Xl; yl) represent the components of the gradient of some potential function
(XI, yl} which satisfies Laplacels equation
2
a 1 (Xl, yl)
ax l2

a 2 1 (Xl, yl)
ayl2

(A-3)

in every region of some irrotational, incompressible, and nonviscous potential flow field free of
sources or sinks. The components of the gradient
'V1 may be written
a'+' l (Xl, yl)
't' ayl = u l (Xl, yl)
a1 (Xl, yl)

ax'

(A-4)

(A-5)

(Xl, yl)

Hence (A-3) can be expressed as
"Vi

Future attempts to increase the accura.cy beyond the present state-of-the-art should consider
some of the aforementioned problems.
Thus, the method of particle trajectory simulation described in this paper which employs an
electrical conducting surface is worthwhile in all
cases except those requiring extremely high accuracy. The simulation is conceptually simple

I...)

au l (Xl, yl)

(Xl, yl)

ox'

oy!

(A-6)

l
WI, u , VI, Xl, and yl represent the non-normalized
components of the gas and particle velocities in
the Xl and yl directions, respectively.

ANALOG SIMULATION OF PARTICLE TRAJECTORIES IN FLUID FLOW

247

If a Reynolds number Re is defined as

I~'I

Zap

g
J-L

(A-16)

= k I~'I

Equation (A-I) can be expressed as

(A-7)

*
{A-8)

Resolving this force into x and y components and
setting the rate of change of n-lon1.enturii equal to
this force, we obtain for the x and y directions
respectively

3
1Ta p V'
P

= !.
aJ-LC R rv' (x' y')
4
D eL.:::'

yil.J

(A-IO)

where 41Ta 3 pp /3 is the mass of the particle and
(x', y') are tlie position coordinates of the particle
within the flow field. Equations (A- 9) and (A-IO)
can easily be rendered to dimensionless form
through some suitable normalization.

(A-II)

(A-IZ)
where

such that it is valid for the range of Re of interest
and determined by experimentally reported
results. 16
Thus we may conclude that there are two
parameters which must be considered when scaling
or analogies are employed: K, and Reo'
Only

*
~~i~:~~:~::t~l::W~' ~::~~:t:r~tdW;~~~~~;t ft~t!~~e

shown that K, often referred to as an inertia
parameter, is the ratio of two lengths Land 1.
L is some characteristic length in the flow field,
say the diameter of a cylinder upon which the
particles impinge (or flow around). 1 is the distance a particle will travel in a quiescent medium
having a viscosity J-L if the particle is in Stokes
flow with initial velocity U. K may be considered
a parameter which is a measure of the degree to
which a particle will respond to a signal (relative
velocity of the gas to the particle) under a given
set of conditions. Large values of K correspond
to particles which will not alter their direction
(due to their inertia) when the gas does (in order
to flow around some object having a characteristic
dimension, L). Conversely, particles having a
low value of K associated with them will not
deviate much from the gas. streamlines of the flow
field. Working with large values of K will not
prove interesting since such particles will travel
in essentially straight lines. Conversely, small
values of K correspond to particles which behave
like gas molecules. Thus, the interesting cases
correspond to K ~ 1.
Appendix B

(A-l3)

U and L represent a characteristic velocity and
characteristic length respectively. The problem
time T, the independent variable in Equations
(A-9) and (A-IO) is related to the dimensionalized
independent variable t, in the normalized Equations (A-II) and (A-IZ) by the following equation

t = (TU)/L

(A-14)

When the Reynolds number, R e , is low (say less
than unity) then the particle is said to be in the
Stokes regime and in this case, we can write:

Details of Error Sources
The error sources which form the driving
functions El and EZ for Equations (37) and (38)
will now be considered. As mentioned in Section
II-C, BVy and BVx will be made up of a sum of
several terms.

Conducting Surface Misalignment

Consider Figure B-1 in which the conducting
surface coordinate axes (Xl, yl) are misaligned
with respect to the X- Y plotter axes (x, y) by an
angle a. For small a it follows that for any fixed
point on the surface

(A-IS)
V

When outside the Stokes regime (Re" 1), Equation
(A-IS) is not valid. We define a function f(Re):

*CD is usually defined for

an object which is not
accelerating. In the case treated here, the particle is accelerating and we will assume that the
same results are applicable.

*
R

Zap U
=~
J-L

x - Xl

- ya

(B-1)

y - y'

+xa

(B-Z)

VXI - aVyl

(B-3)

V, + aVxl
Y

(B-4)

ANALOG APPLICATIONS AND TECHNIQUES

248

The computer positions the plotter to coordinate
(x, y) where the surface voltage is V(x, y). If
OA = OA' and OB = OB' in Figure B-1, then the
errors introduced are

03 Vy

= 4; y ~G 1 y

- 1) tP 1 - (G 4y - 1) tP 4

- 1) tPJ
+ (G Zy - 1) tP Z - (G
3y

(B-14)

(B-S)
6 V
1 y

= Vy

(B-6)

- V'
y'

Expanding V' in a Taylor's series about its operating point for the deviations given by Equations
(B-1) and (B-Z) (for which case V = V'), taking
derivatives with respect to x' and y' and combining the results with Equations (B-1) to (B-6)
yields (neglecting high order effects)
0IV
1:.
~

=CV', +V', ,x-V', ,y1a
L y
xy
xx :J
-

1.y -

rv'x'
L'

_v'• x' y' ,,+ v'y' r..,.lJ
J

•

where Gix and GiJ are the gains on the ith probe
in forming Vx an V y . Once again a Taylor's
Series can be used to determine the tPi's, and
neglecting higher order terms the result is

J
J

03 V x = ('4;X)t G IX + G Zx + G 3x - G 4

tGlX + G Zx - G 3x + G 4x V y

(B-IS)

(B-7)

(B-8)
(B-16)

Probe Angular Misalignment

Consider Figure B- Z. To approximate Vx
and V y ' the computer forms
V

tP Z - tPl + tP3 - tP4
4Ax

(B-9)

tPl - tP4 + tP Z - tP3
4Ay

(B-IO)

Finite Difference Approximation to Voltage
Gradient Components
Here

(B-17)

tPl-~4+tPZ-~3

To compute the values of the tPi' s, the surface
voltage is expanded in a bivariate Taylor's series
about the coordinates (x, y) and the deviations of
the various probe elements from (x, y) is inserted
in the resulting expression under the condition
that there is a probe rotation (3. For example,
the normalized coordinates of the probe that
measures tPI' are [-Ax + (3Ay, Ay + (3Ax]. Having
obtainedthetPi's, Equations (B-9) and (B-IO) are
used resulting in
0ZV

x = -(3Vy

0ZV y = (3Vx
3.

4Ay

Again a bivariate Taylor's Series is used, and
neglecting terms higher in order than the cubics
results in
(B-19)

(B-ZO)

(B-1 1 )
(B-IZ)

Unequal Probe Element Gains

The right hand sides of Equations (B-9) and
(B-IO) are only ideally formed. Each tPi in each
equation is multiplied by a computer gain which
is close to but not exactly equal to one. Thus it
follows that

(B-IS)

where Ax and Ay are the normalized (with respect
to L') distances defined in Figure (B- Z). Equations (B-19) and (B- ZO) show a significant result
in that no linear terms in Ax and Ay appear. Thus
04 Vx and 64V y contain no first order error effects
and in most cases can be ignored. Only in the
immediate vicinity of gas flow stagnation points
will there be any significant error. This elimination of first order effects resulted from using
a four element probe and averaging the voltage
derivatives. It is not a characteristic of arbitrary probe designs.
5.

Conducting Surface Irregularities

This error, denoted by 6 S V x and 0Sv, , is
unavoidable and does not readily lend itse1f to
analysis in the general case of arbitrary conducting surface shapes. A simple example is

249

ANALOG SIMULATION OF PARTICLE TRAJECTORIES IN FLUID FLOW

considered in Section III-C which predicts particle
traj ectory errors statistically given a statistical
description of the surface voltage errors. This
lends insight to the more general case.
6.

The derivation of error sources for the general
error Equations (37) and (38) is now complete.
Equations (B-20), (B-22), and (B-26) to (B-30)
form the driving forces in the determination of
ox and oy.

Errors Caused by the Computer Loading
the Conductive Surface

Appendix C

These errors are negligible in using an uncoated Teledeltos surface since its source resistance was experimentally determined to be about
3K ohms and an unloading circuit pictured in
Figure B- 3, into which each ~i is transmitted can
be adjusted for an input impedance in excess of
1000M ohms.
Adding all the separate error sources the
inputs to Equations (37) and (38) are

Details of Error Sources for Example
This appendix presents a description of the
individual errors comprising the terms in the
"inputs II E! and EZ to the error model.
Approximation of Vx and Vy by finite differences of surface voltages. This error is nonexistant since the third order partials of V are
zero for parallel stream lines.
Conducting surface misalignment. In this
case the terms 01 Vx and 01 Vy reduce to

(B-22)

1 Vx = _VIyl a = -a

(C-I)

6 V = VI a = V a = 0
I Y
Xl
X

Errors Caused by Misaligned Servo
Multiplier Potentiometers Ell' E 12, E 21' E 22

Consider the derivation of Ell, the output
error in the formulation of Wx,.2.
In Figure B-4
91 and 911 represent the ratios of pot rotation
above the center tap to the total rotation above
this point. If pot 1 is misaligned by 100 111 percent full scale with respect to the feedback pot
then

(C-2)

Equation (57) reduces to -a since Vyl is normalized to equal unity in magnitude. It will be
assumed that the surface can be aligned on the
x- Y plotter so that there is less than 1/16 inch
offset at the end of a 20-inch surface edge. This
corresponds to lal:::O. 18 degree.
Probe angular misalignment.
eral equations reduce to

Here the gen-

(B-23)
also
(B-24)

(B- 25)

02 Vx = -{3Vy =-{3

(C-3)

02V

(C-4)

= {3V

= 0

It is assumed that i {31 ::: 1'1/360

= O. 50.

Errors caused by unequal multiplication of
probe element voltages. Here the general equations reduce to

Combining these equations yields
(B- 26)

Similarly it can be shown that
")1/

~ 12 = "' . . 12

I ...

\.0-

""),.,\

£. f

(B-28)

E2l = 21.21Wy

(C-5)

(B-29)
8.

Function Generator Error Ef Is Already
in the Desired Form and Is a Function of w

(B-30)

since the gains can usually be controlled so that
the second term is negligible with respect to
other system errors, and

(C-6)

ANALOG APPLICATIONS AND TECHNIQUES

250

For subsequent convenience Y/Vs (the parameters
being defined in Figure 4) has been introduced
into these equations. This is valid since
Y/Vs = l/v = 1 due to the normalization of V
referred to previously. These probe element
gains are best adjusted by using an amplifier as a
comparator. It is then the difference between
gains that is controlled rather than the values of
the gains themselves. Experience indicates that
the difference between two such gains can be held
well below O. 01 percent. Therefore

IG li - G 3

d:::: o. 0001,

Bibliography
1.

Hoglund, R. F., Recent Advances in GasParticle Nozzle Flows, ARS Paper No.
2331-62, presented at the Solid Propellant
Rocket Conference; Waco, Texas, January
1962, 43 pp.

Malavard, L. C., "The Use of Rheoelectric
Analogies in Aerodynamics, n AGARDograph
18, August 1956.

Logan, B. F., G. R. Welti, and G. S. Sponsler,
Analog Study of Electronic Trajectories,
J. Assoc. Compo Mach., vol 2, pp. 28-41,
1955.

Karplus, W. J., Analog Simulation: Solution
of Field Problems, McGraw Hill Publishing
Co., New York, New York, 1958.

Einstein, P. A., Factors Limiting the Accuracy of Electrolytic Plotting Tanks, Brit. J.
Appl. Phys., vol. 2, pp. 49-55, 1951.

Sander, K. F. and J. G. Yates, A New Form
of Electrolytic Tank, Proc. Inst. Elec.
Engrs., vol. 104, pt. C, pp. 81-86, 1957.

Boothroyd, A. R., E. C. Cherry, and
R. Makar, An Electrolytic Tank for the
Measurement of Steady State Response,
Transient Response and Allied Properties
of Networks, Proc. Inst. Elec. Engrs.,
vol. 96, pt. I, pp. 163-177, 1949.

Softky, S., and J. Jungerman, Electrolytic
Tank Measurements. in Three Dimensions,
Rev. Sci. Instr., vol. 23, pp. 306-307, 1952.

Kallis, C. J., N. H. Freed, and C. L. Suzman,
Conducting Sheet Analogues for the Solution
of Field Problems, Report 1/6 0, Department
of Mechanical Engineering, University of
Witwatersrand, Johannesburg, South Africa,
October 1960.

[G 2i - G 4i J:=0. 0001

for i = x or y.
Conducting Surface Irregularities. These
errors, denoted by 65Vx and 55Vy, are some
random function of the probe coordinates (x, y)
and thus do not remain fixed along a given trajectory like all tIle other errors considered in this
analysis. As mentioned in Section III-C, further
detailed discussion on the statistical description
of these errors may be found in Reference 23.
Servo Potentiometer Misalignment Errors.
From Appendix B, it follows that
s
E12=2112K
S

E 22 = 2122 K

(C-7)

(C-8)

The servos are assumed sufficiently accurate so
that no potentiometer is misaligned more than
O. 1 percent of full scale, therefore:

Summing all the aforementioned errors yields
the following expression for El and E 2 :

E = (G
j

21.12

=" + ~ +
+

the Determination of Particle Trajectories in
Potential Flow Fields, Unpublished term
paper fo::, Course No. ENGP,- 213 B, Uni~.rer
sity of California, Los Angeles, 22 pp. ,
January 1961.

G3Y)(4iy)~)
11.

(G 2y - G4Y)(41y)~)

jy -

10. Norum, V. D., Conductive Solid Analogs in

°5 V y

(-G

(C-9)

G3x)t~)R)

(G 2x - G4x)(41x)Pv;) + 2122

(C-I0)

Hicks, H., and A. Permoda, Uniformly Conductive Surfaces, Icing Research Staff,
University of Michigan, Engineering Research
Institute, Ann Arbor, Mich., 1953.

12. Winiarski, F. J., A.."1 Electronic Analog Computer Input Device for Functions of Two Variables, M. S. thesis, University of California,
Los Angeles, 1955.
13. Martin, R. J., N. A. Masnari, and J. E. Rowe,
Analog Representation of Poisson's Equation
in Two Dimensions, IRE Trans. on Electronic
Computers, vol. EC- 9, No.4, pp. 490 -496,
December 1960.
14.

Larrowe, V. and M. Spencer, Use of SemiConducting Surfaces in Analog Function Generation, presented at the National Simulation
Conference; Dallas, Texas, October 1958,
6 pp.

ANALOG SIMULATION OF PARTICLE TRAJECTORIES IN FLUID FLOW

15. Langmuir, I., and K. B. Blodgett, A Mathematical Investigation of Water Droplet Trajectories, AAF TN 5418, ATI No. 25223, 1946.
16. Brun, R. J., W. Lewis, P. J. Perkins, and
J. S. Serafini, Impingement of Cloud Droplets
on a Cylinder and Procedure for Measuring
Li qui d- Water Content and Droplet Sizes in
Supercooled Clouds by Rotating Multicylinder Method, NACA Report No. 1215,
Lewis Flight Propulsion Lab., Cleveland,
Ohio, 1955.
17. Kowe, J.~., and R. J. Martin, An ElectronTrajectory Calculator and its Component
Poisson Cell, Proc. IEE,-v'ol. 105, pt. B
(Supplement), pp. 1024-1032, 1958.
18. Hollway, D. L., The Determination of
Electron Trajectories in the Presence of
Space Charge, Australian J. Phys., vol. 8,
pp. 74-89, 1955.
19. Brewer, G. R. and T. VanDuzer, SpaceCharge Simulation in an Electrolytic Tank,
J. Appl. Phys., Vol. 30, pp. 291-301,
March 1959.
20. Kliegel, J. R., One Dimensional Flow of a
Gas Particle System, Journal of Aero/Space
Sciences, March 1960.
21. Adelberg, M. and S. Lafazan, Analog Simulation of Two Dimensional Uncoupled Particle
Trajectories in a Potential Flow Field, Unpublished STL Internal Document (Unclassified) No. 7620.3-2, January 1960.
22.

Norum, V. D. , Analog Simulation of Particle
Motion in a Potential Flow Field, Unpublished
STL Internal Document (Unclassified)
No. STL/TM-60-0000-09030, April 1960.

23.

Farrenkopf, R. L., Simulation Error Analysis
of Particle Trajectories in a Potential Flow
Field, Unpublished STL Internal Document
(Unclassified) No. 93l3. 8- 99, August 1961.

24.

Beers, Y., Introduction to the Theory of
Error, Addison-Wesley Publishing Co. ,
Reading, Mass., 1957.

25.

Davenport, W. B. and W. L. Root, An Introduction to the Theory of Random Signals and
Noise, McGraw Hill Book Co., New York,
New York, 1958.

26. Malavard, L., On a New Technique for
Experimental Investigations by Means of
Rheoelectric Analogs, Recherche Aeronaut,

vol. 20, pp. 61-68, 1951.
27. Kriebel, A. R., Particle Trajectories in a
Gas Centrifuge, Transactions of the ASME
Journal of Basic Engineering, Paper No.
60- WA-158.

251

252

ANALOG APPLICATIONS AND TECHNIQUES

15°1

-----I-rh---+-I~"

------+-----------j

1251----1

100

-a.

~Ix
'---'"

25~~---------------+------------------~----~~--------~

Figure 6.

0.015

0.010

0.005

Probability Density Function of Trajectory Error

~______________~____________________________-,~~______________~____________~~iLI

I
I

STREAMLINE

~------~~~~====------~--------~~~--I~I
IMPINGEMENT POINT~ A'

5 INCHES

/'
./
./

~----------4-----------~i------------+----/~------~----------ll

i
i

TYPICAL PARTICLE
i
TRAJECTORY--........ :

__-__-___--__-__- __- _--~~i

A~-__-_-__-__-__-__-__-~t_-

_______ -

-- /

________________+-______________-rr______________ I~
- 5 i~JCHES -~

Figure 7.

Quarter Section of Infinite Flow· Field Distorted by Cylinder

ANALOG SIMULATION OF PARTICLE TRAJECTORIES IN FLUID FLOW

253

1.4L
y
STL SOLUTION - NACA SOLUTION -: - REO = 63.25
PARTICLE AND GAS VELOCITIES IDENTICAL
AT)( =-5L

K=4

1.2L

I.OL

0.8L

~[:7

--==-'
_:=-;:y1

0.6L

OAL

0.2L

-5L

~
~~

-4L
Figure 8.

-3L

-2L

-IL

Particle Trajectories in the Vicinity of a Cylinder of Radius L

1.4L~----------------~------------------~----------------~------------------~----------------~

y
I. 2L I----~-------+-------I

K =0.5
STL SOLUTION - REO = 70.75
NACA SOLUTION - - PARTICLE AND GAS VELOCITIES IDENTICAL
AT )( = -5L

1.0L~---------+----------~----------+---------+7L--~L-~--~~

0.8L~---------+------------~----------r----~~---+,~~H.~----~

0.6LL-----~==:::::::::::::::===:t====----~---_____::;;~~~II_----~
0.4LL------~--""""""'=~::::::~b:=====--~-----____:4U-----~

-5L

-4L
Figure 9.

-3L

-2L

-IL

Particle Trajectories in the Vicinity of a Cylinder of Radius L

ANALOG APPLICATIONS AND TECHNIQUES

254

o
Figure B-l.

A
Conducting Surface Misalignment

Figure B-3.

Figure 3-4.

Figure B- 2.

Unloading Circuit

Servo Multiplier

Angular Misalignment of Probe

255

THE APPLICATION OF FINITE FOURIER TRANSFORMS
TO ANALOG COMPUTER SIMULATIONS
Eric Liban
Grumman Aircraft Engineering Corp.
Bethpage, New York

SUIIl!Ilary

An Analog Computer technique for the
solution of certain classes of boundary
value problems of partial differential
equation based on Finite Fourier Transforms is presented, which requires considerably less computer components than
conventional finite difference methods.
The derivation of the Finite Fourier
Transform method is briefly stated and
then applied to analog computer simulations of heat transfer equations with
linear and nonlinear boundary conditions.
Introduction
A well known method for the solution
of ordinary linear differential equations
with constant coefficients is the Laplace
transform method which reduces the differential equation to an algebraic equation. The solution of the latter is a
function of a parameter "s" and given
initial conditions, and its inverse Laplace transform is the solution of the
differential equation. This method is
easily extended to partial differential
equations in two independent variables.
A Laplace transform with respect to one
of the independent variables gives an
ordinary differential equation, whose solution is the Laplace transform of the
function satisfying the partial differential equation and its initial and boundary conditions. The inapplicability of
this method for analog computations
arises from the fact that the inverse Laplace transform, a necessary step to extract the solution, is an integration
over an infinite path in the complex domain. To solve partial differential
equationson an Analog Computer by a
transform method the inverse transform
must be obtainable by operations in the
real domain only. The particular transform discussed in this paper is the
Finite Fourier Transform, which is applicable to equations in which only the even
order derivatives (of the function) with
respect to the transformed variable ap-

pear. The heat equation, wave equation
and bending beam equation are of such
nature. Many other transforms exist
which may be used for other types of
equations. (Refs. 1, 2, and 3) .
A feature, which makes the Finite
Transform a very economical method for
analog computers, is that the inverse
transform may be solved only for regions
of interest. The truncation error in the
analog simulation may be made smaller
than the error in the amplifiers themselves, and therefore the solution obtained by the Finite Fourier Transform
method is the exact solution within the
accuracy of the Analog Computer; and the
bounds on the deviation from the true solution can be stated precisely in terms
of the usually small amplifier noise and
integrator drifts.
Finite Fourier Transforms
The transform exists for all bounded,
piecewise continuous functions over a
finite interval. The extension of a continuous function F(x) defined for
o < x <~, into an odd periodic function
F(x) ;ith period 2~ may be expressed
by the Fourier series
co

""'
F(x)

f (n)sin nx .
s

(1)

n=l
The coefficients are given by

I
~

(n)

F(x) sin nx dx ,

o
n=l, 2, ... .

(2)

ANALOG APPLICATIONS AND TECHNIQUES

256

This set of coefficients, defined by Eq.
(2), is the Finite Fourier Sine Transform
of t{x) , and the inverse Sine Transform
is F{~) as defined by Eq. (l). Note
~hat
F(x) = F(x) for 0 < x <~. But
F(O) and F(~) will always equal zero,
whatever F{O) and F{~) may be. This
follows from the extension of F(x) into
an odd function and the property of Fourier series to converge at finite discontinuities to the average value of the
limits the function approaches from the
right and left respectively.

2
- n f (n)
c
(6)

- F' (0) + (-l) ~' (71")
by integrating the left side by parts
twice and substituting Eq. (5), F'{O)
and F' (71") are the values of the derivative of F(x) at x = 0 and 71", respectively.

The following expression is obtained

by two successive integrations by parts
and a substitution using Eq. (2):

Two other useful Finite Fourier
Transforms are stated below:
Finite A-Transform

- n 2 f (n)
s

2n-l
F{x) sin -2- x dx ,
(3)

(7)

+ n[F{O) - (-l)~{~)] .
n=l, 2, ... .
into an even funcE~panding F{x)
tion F{x) of period 2~ leads to the
Fourier series

1.71"

F(x)

(O)

Inverse A-Transform
()()

2n-l
fA (n) sin -2- x

F{x)

+ ~71"

f c (n)cos nx

(8)

(4)

n=l

n=l
and
where the set of coefficients fc(n)
the Finite Fourier Cosine Transform
given by

is
(FPC~

71"

(n)

2
.c ,_,
2 ) .LA \11)

2n-l
... ,

,~_~

S1.n

(9)

F(x)cos nx dx ,

+ (2n -l)F(0) - (-l)~' (71") .
2

(5)

n=O, 1, 2, ... .
The inverse FFCT is the function F(x)
as given by Eq. (4). Here F{x) = F{x)
fQr the closed interval 0 < x < 71"; while
dF/dx = dF/dx holds generally only fQr
o < x < 71", since the derivative of F
may be discontinuous at x = n71". The
following relations are obtained for the
FFCT:

Finite

(n)

~-Transform

71"

2n-l
F(x)cos -2- x dx ,
(10)

n=l, 2, ... .

257

THE APPLICATION OF FINITE FOURIER TRANSFORMS TO ANALOG COMPUTER SIMULATIONS

Inverse

I-L-Transform

ature

is given by

'=I

F(x)

1.
7T"

2n-1
fl-L (n) cos -2- x

(11}

n=l

..l2Ml'
Ln-.l
cos -2- x dx
2
dx

~ ~L

(13)

Initial Condition:

and
r7T"

2
dT
d T
dT = a
d~2 '

1'\__

T(O,

2
(2n -1) fl-L(n)
2

(14)

Boundary Conditions:
(12)

- F' (0) + (-1)~(7T")

dT
k d~ = - q(T)

0
(15)

Only the relations expressing the transforms of the second derivative of a function, in terms of the transform of the
function and its boundary values, were
shown. However, relations may be obtained for all even order derivatives.
For an elementary discussion of the Finite Fourier Transform see Churchill,
Modern Operational Mathematics in Engineering.~ For a more advanced treatise
on the Finite Fourier Transform and other
Integral Transforms see bibliography.

dT
d~ = 0

L .

The symbols used in the above equations
are defined in the following table:
T _ temperature - oR
T == time - sec
~ _ space coordinate - in
a == thermal diffusivity - in2/sec
k == thermal conductivity - BTU/sec-in-oR

Analog Simulations of the Heat Equation
The Re-entry Problem
The Finite Fourier Transform method
is applied first to the one-dimensional
heat equation with boundary conditions
encountered in the "re-entry problem".
Let ~ be the space coordinate of a onedimensional slab of length L, which is
the idealization of a longitudinal section of the nose cone of a missile, T
the time and T(T,~) the temperature.
At ~ = 0 a heat input or heat flux is
given, while at ~ = L the slab is assumed to be insulated, that is, the temperature gradient is zero at ~ = L. In
this problem the main interest is in the
temperature of the face ~ = 0, to determine whether it rises above or remains
below the melting point. Also of concern
is the temperature at ~ = L, which must
remain below the melting temperature of
the back-up structure. The mathematical
statement of this problem for homogeneous
slabs with temperature independent thermal constants and uniform initial temper-

q == heat input rate per unit area BTU/sec-in 2
The linear heat equation may be solved
for the temperature deviation from the
initial temperature, expressed by
~)

U(T,

= T(T,

(16)

- T

Equation (16) and the substitutions

x = E ~
L

2
t = a 7T" T
L2

(17)

transform Eqs. (13) , (14) , and (15) to
the equation
2
dU
d U
dt = 2
dX

o < x < 7T"

(18)

ANALOG APPLICATIONS AND TECHNIQUES

258

Initial Condition:

o .

u(O, x)

(19)

Boundary Conditions:
eu
L
ex = - 11"k q(t) - - Q(t)

(20)

x = 11"

Equation (18) and boundary conditions as
shown in Eq. (20) indicate the use of the
Finite Fourier Cosine Transform with respect to x. The FFCT of u(t, x) is
given by

I~ u(t,

(t, n)

under discussion, equals zero. If the
problem were solved for the temperature
T with initial conditions T(O, x) = TO,
then the initial conditions for Eqs. (23)
would still all be zero with the exception of fc(t, 0), since the integral of
a constant times cos nx between 0 and
11" always vanishes when n j O. When the
initial temperature distribution is a
function of x, then the initial conditions for fc(t, n) may be either readily computable by hand or, easily evaluated on the analog computer. The set of
solutions fc(t, n) of Eqs. (23) form the
FFCT of u(t, x); i.e., they are the
Fourier coefficients as a function of
time t of the temperature u(t, x).
The inverse FFCT, as given by Eq. (4),
for x = 0 and x = 11" respectively, becomes:
00

x) cos nx dx ,

u (t, 0)

1
11"

(t, 0)

+1 \

11"

(t, n) (25)

n=l

(21)
n=O, 1,

It is easily seen that

u(t,

11")

1
f (t 0)
11"
C
'
(26)

eu
et cos nx dx

(t, n) ,
(22)

By multiplying both sides of Eq. (18)
with cos nx dx and integrating from 0
to 11" using the notation defined hy Eqs.
(21) and (22), the differential equations
for the terms of the FFCT are formed.
Equation (6) with the given Boundary Conditions as shown in Eq. (20) gives:

2
n f c (t, n)

(t, n)

+1
11"

+ Q(t)
(23)

n=O, 1, 2,

Clearly, it is not possible to solve Eqs.
(23) for all n from 0 to 00. However, the inverse Ftnite Fouri.er Cosine
Transform is a fairly rapidly convergent
series, because it is a continuous function for all x. The coefficients behave
like 1/n 2 for increasing n. When
Q(t) > 0 for all t, it can easily be
seen from Eqs. (23) that fc(t, n) ~ 0
for all nand t. Hence,there exists
an N for any E, no matter how small,
such that

with initial conditions:
maxiu(t, 0)
f

(0, n)

0 ,

n=O, 1, 2, . . . .

(_l)n f (t, n)
c

n=l

n=O, 1, ... .

- 111"

(24)

The initial condition of fc(t, n)
equals the FFCT of the initial condition of u(t, x), which for the case

f c (t, 0)
(27)

_1
11"

n=l

f C (t, n)

E •

THE APPLICATION OF FINITE FOURIER TRANSFORMS TO ANALOG COMPUTER SIMULATIONS

That is, there exists an
the truncation error

such that

max £'IT

f (t, n)

(28)

n=N+l
will be smaller than the accuracy of the
computer or some other desired accuracy
compatible with analog computer characteristics. The maximum absolute errors
in the computer solutions of
1

u(t, x)

'IT

f (t, 0)
c
(29)

N
+£
'IT

f (t, n)cos nx
c

259

less of the number of Fourier coefficients used. This can easily be seen
from the fact that the output voltages of
all the integrators will eventually be
zero, when Q(t)
0, except the output
of the integrator generating fc(t, 0).
When the slab is at uniform constant temperature, then the Fourier series of the
temperature distribution is simply the
constant (l/'IT)fc(t, 0).

Convective Boundary Condition
The boundary with convective heat
transfer may be either ~ = 0 or ~ = L,
or both. In addition a heat input q(T)
may be given. In this section the analog
simulation of the heat equation is shown
for the following boundary conditions:
k dT

- q(T)

k dT

h(T(T, L) - T.)

L , (32)

(31)

n=l

for x ~ 0, will all be smaller than
since for positive fc(t, n)

EO'

where
00

h
max £
'IT

f c (t, n) cos nx
n=N+l
(30)
00

< max l.'IT

(t, n)

n=N+l
The number of Fourier coefficients to be
generated on the analog computer may
therefore be obtained by an a priori estimate or by increasing N until
fc(t, N) ~ 0 for all t. Figure 1 shows
the analog computer setup for the Finite
Fourier method solution of Eqs. (18),
(19), and (20) with N = 7. For test
purposes the heat input Q(t) was a
steep saw tooth and it was found that the
temperature at x = 0 for all time t
differed always by less than 1% from the
analytically obtained exact solution.
The slab assumes a uniform steady state
temperature when the heat input is of
finite duration. The Fourier Transform
method of simulation will always give the
correct steady state temperature regard-

convective heat transfer
coefficient - BTU/in 2 sec of.

The boundary conditions, stated in words,
mean that the bar is heated at the rate
q(T) at the face ~ = 0 while the face
~ = L
is in contact with a substance at
temperature Ti' which may be a function
of time, and heat is transferred from the
bar to this substance according to Eq.
(32). Let the bar be initially at a uniform constant temperature T(O, ~) = TO.
With the substitutions Eqs. (16) and (17),
ui = Ti - TO, and (L/'lTk)q(t) = Q(t)
the problem is stated:
t

(33)

Initial Condition:
u(O, x)

o .

(34)

Boundary Conditions:
- Q(t)

(35)

ANALOG APPLICATIONS AND TECHNIQUES

260

dU = -L h [ u(t
-dX
~
,

- u.1 ]

(36)

Since the boundary conditions prescribe
the derivatives at

and

~ ~,

the use of the Finite Fourier Cosine
Transform is indicated; and from Eq. (6)
and the above boundary conditions is obtained the set of differential equations

= - n 2 f c (t, n) + Q(t)

f (t, n)
c

(-1) n

b h fu (t. ~) - u. 1
~

(37)

The Flat Plate Radiating into Vacuum
The term IIf1at p1ate" is taken here
to mean a solid slab bounded by a pair of
parallel planes ; = - Land ; = L.
The initial temperature TO is uniform
and Stefan-Boltzmann radiation into vacuum takes place at the two faces ~ = ± L.
Clearly, the temperature distribution
will be symmetrical about ~ = 0 and
therefore it is more convenient to state
the problem as follows:
dT

2
d T

d~2

~ ~ L

(39)

n=O, 1, 2, ... .
Condition:

T_.! ...... ..: _1

.1.U.1.L..1.Cl.1.

The essential difference between Eqs.
(37) and the equations for the Fourier
Transform of the heat equation with insulated boundary Eqs. (23) is that now the
boundary condition is a function of the
temperature at x =~. But u(t,~) is
given by Eq. (26), as in the previous example and may be generated continuously.
Hence the last term of Eq. (37) is easily
formed and fed back to the appropriate
integrators in the simulation. The analog circuit for the heat equation with a
heat input on one face and a convective
heat transfer at the other face is shown
in Fig. 2. The FFCT was solved for
n = 0 to n = 7.
Radiation Heat Transfer 5
Examples chosen for this type of
boundary conditions are a flat plate and
a sphere radiating in a vacuum. The
boundary condition for radiation heat
transfer at the face ~ = L is given by

T(O,

(40)

Boundary Conditions:
dT

- oE[T(T, L)]4 at

(41)

L (42)

Equation (41) follows from the symmetry
condition, and Eq. (42) is obtained from
Eq. (38) by letting Ta = 0 for radiation into vacuum. Since Eq. (42) is nonlinear it can no longer be solved for the
temperature deviation from the initial
temperature TO' It is probably just as
simple to simulate the original equations,
and certainly the results would be more
easily interpreted; however, for simplicity of presentation let
x

(38)

1L ~
L

and

a L

(43)

where
and set
o
E

_ Stefan-Bo1tzmann's constant BTU/sec in 2 °R4
_

emissivity - dimensionless

Ta - temperature to which surface
radiates - oR.

b
'Tf

EO U

(44)

and
u

(45)

261

THE APPLICATION OF FINITE FOURIER TRANSFORMS TO ANALOG COMPUTER SIMULATIONS

The problem may now be stated
t

§£here Radiating Into Vacuum

•

(46)

Initial Condition:
1

u(O, x)

The heat equation for a sphere with
temperature distribution a function of
time T and distance p from the center
of the sphere, expressed in polar coordinates is given by

(47)

a a
02 op
,-

cJT

(

aT)

(52)

Boundary Conditions:

au
ax

By the change of variables
at

x = 0

(48)
r =

au
ax

4
- gu (t,

7r)

x =

t = a

u = r ..I..
TO

(53)

(49)
where R is the radius of the sphere,
Eq. (52) becomes

The differential equations for the FFCT
are derived in the same way as in the
previous examples and are given by
- n

2 f (t, n)

- (-1) n

gu4( t , If)

(54)

for
(50)

< r < 7r

and

> O.

Initial Condition from Eq. (53):

n=O, 1, 2, ... .

u(O, r) = r

The initial conditions of fc(t, n) are
the FFCT's of u(O, x), which for
u(O, x) = 1 equals 7r when n = 0, and
equals zero for all n ~ O. The last
term in Eq. (50) is generated continuous1y from

(55)

The radiating boundary condition as given
in Eq. (38) becomes

au
or

= u(t,

7r)

gu (t, If)

r =

(56)

where
u(t,

7r)

1
-7r f c
(t' 0)
(51)

(57)

+.£
7r

(-1) n f (t, n)
c

n=l

raised to the 4th power, which in the
simulation indicated in Fig. 3 was performed by two successive servo-multiplications. The simulation proved to be
stable and in agreement with the solution
obtained by Abarbane1. 5 If boundary Eq.
(42) were replaced by Eq. (38), the simulation would differ only slightly.

Boundary Condition:
u(t, 0) = 0

r = 0

(58)

Equation (58) insures that the temperature T(T, 0) remains finite. In this
case the temperature is prescribed on the
boundary r = 0 while at the boundary
r = 7r the temperature gradient au/ar
is a given function of the temperature.
The Finite A-Transform, as given by Eq.
(7), is to be used for these boundary

ANALOG APPLICATIONS AND TECHNIQUES

262

conditions. From Eqs. (9), (56), and
(58) one obtains the following set of
differential equations

Since initially u(t, If) = If from Eq.
(53), one can perform a steady state
check on the computer setup and on the
convergence of the truncated series;
namely, from Eqs. (61) and (64)
(59)

- (-1) n [ u ( t , If)

- gu ( t , If)]

1
If

(65)

On the analog computer (as well as numerically) 2% accuracy T~y be achieved with
eight coefficients. The analog simulation is shown in Fig. 4.

From Eq. (8)
()()

f,(t,
n)sin(n 1\

u(t, r)

~)r

(60)

n=l
and
()()

u(t, If)

n=l

1, 2, ... .

(n - ~)

~\
"L

-( -1) n

fA (t, n)

(61)

n=l
Equation (61) is used in the simulation
to form the last term in Eq. (59). From
Eq. (53) the temperature at p = R is
given by
TO
-:;- u(t, If) .

T(t, R)

(62)

The ini.tial conditions f~\(O, n)
tained from Eqs. (55) and (7) by

are ob-

~)r

dr ,
(63)

n=l, 2, .•. , N
which upon integration becomes
1
2
-(-------1)
(_l)n
n - "2

(64)

n=l, 2, ... , N

Problems with convective as well as
radiating boundary conditions prescribed
may be solved by this method by the obvious extension of combining the convective term h(u - ui) and the radiation
term g (u4 - ua 4) in the differential
equations generating the Finite Fourier
Transforms. The temperature at points
other than the boundary, if they should
be needed, may be readily obtained by
summing the Fourier coefficients weighted
by their proper trigonometric terms.
This simply requires a potentiometer for
each term and an inverter when necessary.
For convection and for radiation the temperature at the boundary should be as
accurate as possible, because the boundary conditions themselves are given by
them. The Finite Fourier Transform method which gives the exact boundary temperature

~AJithin

the computer accuracy"" can be

very successfully applied.

r sin(n -

Concluding Remarks

The most widely used methods for the
solution of partial differential equations are based on finite differences.
These methods require certain assumptions
about where the finite difference equals
the derivative which by necessity have to
be most loosely made on the boundaries;
the very points where the greatest accuracy is required. One must form many grid
points, at least, near the boundary in
order for the solution of the difference
equation to come close to the solution of
the differential equations. For substances with low conductivity, as used
for nose cones in missiles, the spacing
of the grid points become even more

THE APPLICATION OF FINITE FOURIER TRANSFORMS TO ANALOG COMPUTER SIMULATIONS

critical.
The Finite Fourier Transform method
may also be used for equations with more
than one space variable. Stephens and
Karplus 6 have employed this transform for
analog simulations of two-dimensional
diffusion equations. Two approaches are
given in their paper. In the first only
one space variable is transformed, which
reduces the given problem to a partial
differential equation with one independent space variable. This they solve then
by a finite difference method. In the
second approach the dependent function is
transformed with respect to both space
variables, thus producing a system of
ordinary differential equations. In
principle, this method may be extended to
analog simulations of heat equations in
three space variables. The number of
ordinary differential equations, however,
becomes quite large when Fourier transformations are performed with respect to
three variables. Their analog simulation
would be practical only if the analog
computer is capable of time sharing or
repetitive modes of operation, and possesses dynamic storage elements. The
Finite Fourier Transform method may also
be a very efficient technique for the solution of multidimensional heat equations
on a linked Analog-Digital computing system. 7
The number of amplifiers required
for the solution of the heat equation by
the Finite Fourier Transform method is
about one-half to one-fifth of the number
of amplifiers needed for a finite difference simulation of equal accuracy. The
ratio depends on the shape of the heat
input curve, the thermal constants, and
the physical dimensions.
References
1.

Sneddon. I.N .• "Fourier Transforms. II
McGraw-Hill, New York, 1951.
'

Tranter, C.J., "Integral Transforms
in Mathematical Physics,1I Wiley &
Sons, Inc., New York, 1956.

Leonard, J.L., flIntegral Transforms
for Application to Partial Differential Equations,1I Grumman Aircraft
Engineering Corporation, Research Department Report RE-I03, September
1958.

263

Churchill, IlModern Operational Mathematics in Engineering,1I McGraw-Hill,
New York, 1944.

Abarbanel, P.S., "Time Dependent Temperature Distribution in Radiating
Solids,1I Journal of Mathematics and
Physics, Vol. 30, 1960.

Stephens, P.A., Jr. and Karplus W.J.,
IIApplication of Finite Integral
Transforms to Analog Simulations,1I
AlEE Transactions, Vol. 78, Part I,
1959.

Burns, A.J. and Kopp, R.E., IICombined
Analog-Digital Simulation,1I Proceedings of the Eastern Joint Computer
Conference, December 1961.

ANALOG APPLICATIONS AND TECHNIQUES

264

-Q (t)

f,. (t,7)

7r'( u(t,O)

'lJ

I~~I
~

Fig. 1 - Analog Simulation Of The Re-entry Problem

Fig. 2 - Heat Equation With Convective Boundary Conditions

THE APPLICATION OF FINITE FOURIER TRANSFORMS TO ANALOG COMPUTER SIMULATIONS

_gu 4 (t,7T)

Fig. 3 - Flat Plate Radiating Into Vacuum

I.e.: 40.0

Fig. 4 - Sphere Radiating Into Vacuum

265

ANALOG SIMULATION OF THE RE-ENTRY OF A BALLISTIC MISSILE WARHEAD
AND MULTIPLE DECOYS
L. E. Fogarty and R. M. Howe
University of Michigan

Ann Arbor, Michigan

Summary
The basic problem considered here is the
computation of the reentry trajectory of a single
ballistic missile warhead as well as the trajectories of a number of decoys which originate
from the warhead trajectory. Suitable three dimensional equations of motion are presented for
a reentry vehicle with arbitrary drag coefficient,
mass, and area, and the analog computer circuit
for solving these equations in real time is given.
Then a method of using several such circuits to
compute simultaneously the trajectories of multiple targets with variations in all three initial
velocity components as well as variations in ballistic coefficient is presented.

Introduction
One of the more interesting current problems in simulation involves the computation of
the trajectories of a very large number of reentry vehicles, each starting with the same position coordinates and approximately the same velocity coordinates, but with the possibility of
widely varying ballistic coefficients. For example, this is the problem presented in the simultaneous simulation of a reentering ballistic
missile warhead and a large number of decoys.
In this paper we will show first how each trajectory can be computed in real time using a modest
amount of .analog computing equipment. If we
compute decoy traj ectories for the extreme upper
and lower limits of velocity perturbations and
ballistic coefficient variations, then simple linear or second order interpolation can be used to
obtain the trajectory for any decoy with intermediate velocity or ballistic coefficient variation.
The required averaging and summing operations
can be accomplished using simple passive resistors. The net result is that a reasonable amount
of analog equipment, a s needed to generate the
limiting trajectories, can be used as a basis for
simultaneous generation of hundreds of decoy
trajectories
First we will consider the appropriate
equations of motion for a single reentering particle. The analog-computer solution of these

equations' will then be presented using a mechanization with solid- state nonlinear components.
This adds the possibility of high speed repetitive operation, although for simulation purposes
real time computation would be more appropriate. Finally, the technique of generating a very
large number of trajectories from several limiting trajectories will be described.

Equations of Motion in the Trajectory Plane
It will be assumed that for purposes of this
simulation the rotation of the earth can be neglected. Although this assumption is not in any
way necessary to implement a practical analog
solution, it simplifie s the equations and henc e
the computer mechanization of the problem.
The actual errors in trajectory as viewed
from a position near the impact point a s a result of this assumption will be quite small compared with the total trajectory distance traversed in the simulation.
With the above assumption the trajectory for
a pure drag vehicle will lie in a vertical plane
through the center of the earth. We can use
polar coordinates r, S in this plane to describe
the position of the warhead, which we will assume is a point mass m (see Figure 1). We denote the horizontal velocity component by Dh
and the vertical velocity component by Wh
(positive downward). Summing forces in the
horizontal and vertical directions, we obtain

m(rS + 2rS) = X

..
·2
m{r - rS )

(1)

2
mgoro
r

- Z

(2)

Here X and Zh are horizontal and vertical
forces Hue to aerodynamic drag, and go is the
acceleration due to gravity at a fixed distance,
r 0' fron: the center of the spherical earth. The
term 2rS in Eq. (1) is the Coriolis acceleration,
whereas re 2 in Eq. (2) is the centrifugal acceleration.
The terms r8 + 2r8 in Eq. (1) can be rewritten as 1/ r d/ dt(r 2 e). Thus the equation can be

268

ANALOG APPLICATIONS AND TECHNIQUES

integrated to give

t
mr

e = J(" r

2
X. dT + mr e]t

(3)

R is the radius of the spherical earth. Eqs. (5),
(6), and (8) through (12) are the basic equations
for motion in the plane of the trajectory. Scaling
of these equations for the computer is simplified
if we introduce a dimensionless radial distance p
and a perturbation 0 p given by the formulas

This is the well known angular momentum integral. We note that
(4)

Thus Eqs. (2) and (3) can be rewritten as
2
g r
W =\(~
h J
2
t

(13)

- 1

=.Vr;-g-0 0

D·

(5)

(14)

It is convenient to define dimensionless velocities

in terms of U

and
Uh

From equation (5) with W = Wh]t=o = Zh = X
h
= 0 we note that a satelliteh in a zero- drag circular orbit at radial distance r 0 will have a velocity
U ho given by

I't

= r/r o ,

=~S
r

rUhh=o
dT+-r

(6)

The aerodynamic drag force D will be directed opposite to the warhead total velocity vector, as shown in Figure 2, and is given by

= Va /U h

= -2p a V a C D A

wh
(7)

where p is the atmospheric density, V is the
total verocity, CD is the drag coefficie8t, and A
is the characteristic area on which the drag coefficient is based. CD will in general be a function of Mach number M, although it may be sufficiently accurate for purposes of this simulation
to assume that CD is constant. The drag components X h and Zh along the horizontal and vertical (downward) directions are given, respectively, by

(10)

Finally, we will assume an exponential atmospheric model. Thus let
(11)

[1+

2
Zh
dT
0 P - u h ) + mg ] T
0

(16 )

and

U
= 1- h 1 + 0P

P oU h

(1+op) - h

dT0

0
+--1 + 0P

(17)

where p and uh are the initial values of p and
uh and w~ere T Ps a time constant equal to the
reciprocal of the circular-orbit frequency and is
given by
T

where the total velocity Va is given by

(15)

In terms of the dimensionless variables of Eqs.
(13) and (15), Eqs. (5) and (6) become

Thus let

=.1
rig
V
0

(18)

For typical ballistic reentry trajectories the
altitude at initiation of trajectory simulation may
range as high as 200 statute miles. If we choose
100 statute miles a s the altitude of the circular
reference orbit, then r = 3950 + 100 = 4050
statute miles and r ranges between 4150 miles
initially and 3950 miles at impact. Thus 0 p in
Eq. (13) ranges over ± 100/4050 = ± 0.025.
Therefore we will neglect 0 p everywhere in Eqs.
(16) and (17) as being small compared with unity
except in the term [(1,+ op )-1 - u~] , where we
approximate
+ op )-1. by 1 - op, and the term
uh (1 + 0 P ) - which we also approximate as
0
uh (1 - 0 p ). Then Eqs. (16) and (17) become

where the aliitude h is given by
h=r-R

(12)

S
0

[1 - 0 p - u

2
Zh
+ -]
h mg
o

dT +
]
-T w h t=O

(19 )

ANALOG SIMULATION OF THE RE-ENTRY OF A BALLISTIC MISSILE WARHEAD AND MULTIPLE DECOYS

269

and
Xh
log (- - )
mg o

(20 )
In addition, we note that
d(op)
d(tl T)

- O. 434

+ log u
(21)

= -wh

For ro = 4050 statute miles the time constant
T = 837 seconds.
Let us assume that we desire to measure
the position of the warhead in the plane of the
trajectory using dimensionless rectilinear coordinates x and y, as shown in Figure 3. If 1000
statute miles is approximately the maximum value for horizontal target distance r x, then the
maximum value of 9 in the figure ?s approximately 0.25 radians or 14 degrees, in which case
small-angle geometry can be used to compute x
and y. Thus if we integrate local horizontal velocity U h u h directly, we obtain, approximately,
the dista

en
-;

l400.000

~300.ooo

()

--j300,000
I

Nomina! Trajf!Clory

l400,OOO

f'T1
::0

f'T1

~
IJ)

z
()
f'T1

'200,000
Co A/mgo6 !---,--- .....

Nomina! Trajectory

CD A /mgo 601-_--l-L..A

100,000

-500

-400

-300

-200

-100

roX (STATUTE MILES)
roX(STATUTE MILES)

Figure 6a.

Figure 6b.

Effect of Initial Vertical Velocity
Perturbation and Different
CDA/ mg on an ICBM Trajectory
o

Effect of Initial Horizontal
Velocity Perturbation on an
ICBM Trajectory

r
7r
I

....IlJ
IlJ
Li.

'Q
)(

t(SECONDS),42 x REAL TIME

J
l

-100

If)

IlJ

...J

'Oints Based on Linear Interpolation
of Log (CoA/mgo ) Between
CoA/mgo·' and 0.01

~ -200

'Points Based on Linear Interpolation
of Log (CDA/mgo ) Betwe~n
CD A/mgo·1 and 0.01

t:i

~-300
x

~ -400 v~

COA/mgc" I, 0.1,0.01

I
-500

t(SECONDS),42x REAL TIME

Figure 7.

Effect of CDA/ mg

ANALOG SIMULATION OF THE RE-ENTRY OF A BALLISTIC

~ISSILE

WARHEAD AND MULTIPLE DECOYS

277

7
t(SECONDS),42 x REAL TIME

-..

2
0,

x
>-

-100
...J

~
....

ul1o= +512 ft/sec

\...

~._

~:::~~'~

,,,..
I.

I_u

8ul1o = -512 ft/sec

'Points Bosed on Linear Interpolation
Between Curves for 8ul1o=z512 ft/sec

-200

....
::>

,\1

en
w

It)

-300

-400

t(S~CONDS), 42 x REAL TIME

Figure 8.

Effect of Initial Horizontal Velocity Perturbation

7
t (SECONDS),42 x REAL TIME

6
0

....
's!

It)

)(

-100
CIl

200

....w
::>
....4

.07999

- .02563

- .04055

.11925

- .00207

- .02511

Activity

-.02846

-.02563

lmalysis

.04004

- .04055

- .00207

Anxiety

.07999

.11925

- .02511

Figure 3.

A Portion of the Correlation
(Term-Term) Matrix

.03022
.03022

THE CONSTRUCTION OF AN EMPIRICALLY BASED MATHEMATICALLY DERIVED CLASSIFICATION SYSTEM

Note that the diagonals in Figure 3 are blank.
The diagonal value expresses the correlation of
the term with itself, i.e., the co~ality of the
term. By communality is meant the portion of the
term's variance which is shared with other terms
and not its unique component. There are a number
of methods which can be used to estimate the commonality. The simplest procedure is to choose the
highest correlation coefficient from among the
other correlations in that set (p. 86-87(1)). Although this method is crude and tends to underestimate the connnunality, it has been shown to be
an adequate method when dealing with a large number of variables. In this study, the highest correlation coefficient in the column was used as the
estimate of the communality.
It is worthwhile to re-emphasize at this
point that the correlation matrix is completely
determined by the empirical data and not by any a
priori assumptions on the point of the investigator. "Ability" and "achievement" occur relatively frequently in the same document and so are
highly correlated. Clearly, if we were able to
group together the related terms, we would have a
type of classification system, for we would be
able to state that, for example, documents dealing
with ability and documents dealing with achievement are likely to be in the same area of discourse. However, this is not a task that can be
done by inspection. In the 90x90 matrix, which is
symmetrical, we have 4,005 correlations
(N(N - 1)). In order to analyze the data in a
2
precise fashion, we employ the technique of factor
analysis
2.5

Factor Analysis

The technique of factor analysis is based
upon matrix al~ebra. The procedures are described
by Thurstone ( ) and more recently by Harman(l)
who also discusses the use of electronic computers
as a comput~nal aid. In this study, the calculations were performed on the IBM 7090 using programs available at the System Development Corporation.
The purpose of factor analysis is to reduce
the original correlation matrix to a smaller number of factors. A factor corresponds to the
eigenvector. The size of the eigenvector, i.e.,
the eigenvalue, is equal to the contribution of
the variance made by that factor: The first
eigenvector, or factor, accounts for a relatively
large proportion of information and each succeeding factor accounts for less. In factor analysis
it is not necessary to account for the total variance of the correlation matrix, for we know that a
certain proportion of the variance is unique or
specific to the given set of documents in the experimental situation. We are only interested in
the common variance, that portion of the variance
that is due to the relationship among the terms
and which would continue to be true for all sets
of documents. The problem, of course, is to determine the proportion of the total variance which is
common. Another way of stating this problem is to

285

pose the question as to when to stop factoring.
Unfortunately, there is no exact answer to
this question, but a number of empirical rules
have been developed as guides for determining the
number of factors to be extracted in any given instance. In essence, these rules are based upon
(a) some previously acquired knowledge of the
domain, and (b) the amount of variance accounted
for by the factors. Since this study is an exploratory one and we had no previous knowledge of
the domain, a conservative approach was taken.
First we extracted factors (eigenvectors) until
the eigenvalues became negative. This resulted in
53 factors which accounted for all the common
variance among the terms as indicated by their
correlation coefficients and with the highest correlation value in the diagonals. From these we
selected the first four factors which accounted
for approximately 30 per cent of the-variance;
the first ten factors, which accounted for about
62 per cent; and the first 18 which accounted for
somewhat more than 90 per cent of the variance.
This gave us three sets of factors. We
interpreted all three, compared all three, and
made the final selection on the basis of which set
provides the most meaningful framework for classification.
The first step in interpretation consisted
of rotating these factors mathematically. By
rotation is meant the process of moving the factor
axes and their hyperplanes in order to allow more
points to fallon these hyperplanese It is obvious that the location of axes by which we describe points in space is arbitrary. Take, for
example, the measurement of latitude and longitude
which is a grid system and one which could be
started anywhere. In longitude, we begin at
Greenwich, which is of historical importance but
has no real significance. Latitude, on the other
hand, is fixed with reference to real features-the poles and the equator. The scientist using
factor analysis cannot be content with factors
that are merely mathematical conveniences. He
wants each factor to correspond to some meaningful
dimension of his problem space. Therefore, he
rotates the factors, i.e., he moves the origin and
angle of the grid system so as to obtain a meaningful position. Meaningfulness is determined by
the criteria of simple structure of the factor
domain. In recent years, a number of analytic
methods of rotation have been developed which
approximate simple structure. In this research
project, the orthogonal varimax solution was used.
Three separate rotations were madej one for 4
factors, one for 10, and one for 18 factors.

Interpretation of the Factors

Factor rotation is designed to locate the
reference axes in a grid system such that each
factor can be meaningfully interpreted. The
interpretation must be made by the investigator
and is based upon his knowledge of the analytic
procedures and the subject matter. There is,
therefore, a degree of subjectivity in the names

INFORMATION RETRIEVAL

286

selected for each factor. These names may be regarded as hypotheses about the factor meaning.
In the 4-factor system, each factor was bipolar making a total of eight dimensions. The
last factor was poorly differentiated. In general,
it was felt that this was not an adequate set of
dimensions.
On the other extreme, the 18-factor system
resulted in a number of factors based on a close
association of a few words, but which could not be
interpreted as underlying dimensions of psychological literature. So that, for example, Factor No.
1 was highly loaded on the two terms--girls and
boys--and Factor No. 4 pointed out the relationship between college and student. In addition,
there seemed to be more than one factor dealing
with the same subject matter. The 18-factor
system leads to too fine a discrimination for this
first eA~loratory study. After reviewing all
three sets of factors, it was felt that the most
reasonable interpretations could be made for the
10-factor system.
Insofar as the actual mechanics of interpreting factors are concerned, the first problem
that one faces is to decide the value of the factor loadings which are to be considered. The
loadings were arranged in order of descending magnitude and therefore on a descending scale of
significance. The vast majority of the loadings
were below .10 and these were considered as not
significant. We tried to restrict our interpretations to factors that had loadings greater than
.20, but in some few instances we did look below
that point. In those cases where the high loadings were negative, we reflected the factor so as
to make them positive. There were no true bipolar
factors; although some factors had one or two
moderately significant negative loadings. These
were not interpreted.
Listed below are the significant loadings
for each factor, together with its name and
interpretation.
3.1

Interpretation of Each Factor

3.1.1

Factor No. 1

3.1.2

Term No.
52
40
27
84
26
89
30

Term No.

Word

Factor Loading

33
10
70
2
63

girls
boys
school
achievement
reading

.74
.73
·30
.20
.18

Five terms had significant loadings on this
factor. Underlying these five terms is a concept
dealing with the achievement of boys and girls in
school. The fact that "reading" is on the list
while "college" is not, leads one to infer that
this factor deals with elementary school achievement.

Word
perception(ual)
learning
experimental
theory
evidence
visual
field

Factor Loading

.46
036
.29
.25
.24
.23
.21

This factor is concerned with experimentation,
theories, and evidence, particularly in the areas
of perception and learning.
3.1.3

Factor No.2. Social Psychology and
Community Organization

Term No.

Word

Factor Loading

49
17
77
90
30
4
73
67
38

organization
community
structure
workers
field
analysis
social
role
job

.67
.54
038
.22
.15
.15
.11
.10
.10

The high loadings deal with community structure and organization. Looking further down the
list of significant terms we see that this factor
is also concerned with social roles, work, field
analysis, etc., all of which are involved in social
psychology.
3.1.4

Factor No. 4.

Studies of College Students

Term No.

Word

Factor Loading

78
16
34

student(s)
college
group(s)
mental
factor( s)
teacher
intelligence
personali ty

·71

Academic Achievement

Factor No.2. Experimental Psychology-Perception and Learning

28
81
37
55

.. (0

.17
.16
.15
.14
.11
.10

The terms that define this factor are the
words "student" and "college." The factor apparently groups together all studies involving
college students whether they deal with teacher
training, intelligence, personality, etc. In
contrast with Factor No. 1 which has to do exclusively with school achievement of boys and
girls, this factor (No.4) has a more varied subject matter as indeed it should, for the interests
of college students are more diverse than academic
achievement.

THE CONSTRUCTION OF AN EMPIRICALLY BASED MATHEMATICALLY DERIVED CLASSIFICATION SYSTEM

3.1.5

Factor No.5.
ing

Term No.
58
23
14
50
35
81

36
70
20

School Guidance and Counsel-

Word

Factor Loading

program
education( al)
child (children)
parents
guidance
teachers
information
scbool(s)
counseling

• 42
-36
-33
.29
.29
.28
.27

.25
.20

It can be seen that while school and education have significant loading on this factor,
the emphasis is on parent-teacher-child guidance
and counseling.
3.1.6

Factor No.6.
Psychotherapy

Term No.
87
59
15
62
12
69
85
34
60
20

Clinical Psychology and

Word
treatment
psychiatric
clinical
psychotherapy
case(s)
schizophrenia
therapy
group(s)
psychoanalysis
counseling

Factor Loading
.44
·35
-32
.22
.16
.16
.16
.12
.12
.11

This factor is clearly concerned with the
treatment of mental disorders which is part of
clinical psychology.
3.1.7

Factor No. 7.

Term No.
2
1
19
68
34
63
37
83
70

Educational Measurement

Word
achievement
ability
correlation
scale
groupe s)
reading
intelligence
teste s )
school(s)

3.1.8

287

Factor No.8. General Psychology-Psychology as a Science
Factor Loading

Word

Term No •

social
research
science
psychological
status

73
65
71
61
75

.42
-32

·31

.25
.24

T'nis factor is best 1a1Je1ed "General
Psychology," for it deals with the broad general
areas of social science and psychological research.
3.1.9

Factor No.9.

Developmental Psychology
Factor Loading

Word

Term No.

emotional
development
cerebral
child (children)
theory
life
nature
factor(s)

25
22
13
14
84
42
47
28

-32
-32
.23
.22
.19
.18
.18
.18

High loadings on "development," "emotional,1I
"cerebral," and "child (children)" help define the
diSCipline with which this factor is concerned as
developmental psychology.
3.1.10

Factor No. 10.
Word

Term No.
54
12
85
41

Therapy:

personal
case( s)
therapy
level

Case Studies
Factor Loading
.56
.55
.42
.21

Factor Loading

.46
.36
·35
·32
.22
.20
.20
.20
.19

The common element present in the terms with
high factor loadings is the measurement of
academic ability. The presence of the words
"correlation," "scale," and "test" helps define
this factor and differentiate it from Factor No. 1
which we labeled "Academic Achievement."

While there appears to be some similarity
between this factor and Factor No. 6 which was
labeled "Clinical Psychology and Psychotherapy,"
the distinctive feature in this factor is the
emphasis upon the words "personal" and "case."
These terms imply an emphasis on case studies, as
part of therapy, and with a rich literature of
their own.
4.

Discussion

Figure 4 lists, in summary form, the names
applied to each of the ten factors, and compares
these to the subject classification used by the
American Psychological Association. There is a
high degree of similarity, as logically there
should be, but there are also some very significant differences. Educational psychology, as a
classification category, seems to be quite broad
and includes four of the ten factors. The factors
also cut across categories, so that Factor No.2,
IIExperimental Psychology--Perception and Learning,r'
is covered by two subject classifications, namely,
"Complex Processes," and IIReceptive and Perceptual

288

INFORMATION RETRIEVAL

Subject Classification-Psychological Index

Factor Name
1-

Academic Achievement

Educational Psychology-School Learning

Experimental Psychology-Perception and Learning

Complex Processes and Organizations-Learning and Memory

3·

Social Psychology and
Community Organization

Social Psychology-Social Institutions

Studies of College Students

(Educational Psychology)

5· School Guidance and Counseling

lJ.

Clinical Psychology and
Psychotherapy

Educational Psycholo~y-Educational Guidance
Clinical Psychology, Guidance,
CO'UIlselir...g----

Diagnosis and Evaluation,
Treatment Methods

7·

Educational Measurement

Educational Psychology
Educational Measurement

General Psychology
--Psychology as a Science

General Psychology-Theory and Systems, Methods,
Professional Problems

9·

Developmental Psychology

Therapy:

r. Behavior Deviations

10.

Case Studies

Unmatched Headings

Figure 4.

Physiological Psychology

Personnel Psychology

Industrial and other Applications

Comparison of Factor Names
and APA Subject-Heading Index

THE CONSTRUCTION OF AN EMPIRICALLY BASED MATHEMATICALLY DERIVED CLASSIFICATION SYSTEM

Processes." On the other hand, there are some
classification headings which do not have comparable factors. The most important of these are
"Personnel Psychology," and "Industrial and Other
Applications." Why this is so is not clear, but
one can hypothesize two explanations: either the
writings on these topics are not unique, and so
can be better subsumed under one or more of the
categories, or the sample of documents was neither
adequate enough nor representative enough to bring
out this factor. In our present state of knowledge, we do not have sufficient information to
choose between these alternatives.
This research study has demonstrated a procedure for grouping documents on the basis of
their similarity as determined by the words in the
text and not on any a priori logical hierarchical
scheme. This does not mean that these ten factors
are the best categories for grouping psychological
literature. Before this can be determined, additional studies of a similar nature would have to
be undertaken and the reliability of the factors
established. This study was exploratory in nature
and was primarily concerned with procedural problems. The obtained results establish the efficacy of the methodology.
5.
5.1

While the usefulness of the method of factor
analysis for empirically deriving a classification
system has been demonstrated, the reliability of
the results needs further testing. It is proposed
that an additional sample of data be factor analyzed and the factors compared. Actually, three
or four such replications would be necessary before a consistent set of factors emerges.
5.2

Psychology." It is hypothesized that this type of
probabilistiC indexing will result in increased
information retrieval effectiveness. This is an
area which warrants serious investigation.
6.

References
(1)

Harman, H. H., Modern Factor Analysis,
University of Chicago Press, Chicago,
lllinois, 1947.

(2)

Maron, M. E., Kuhns, J. L., and Ray, L. C.,
"Probabilistic Indexing,1t 'IM No.3, RamoWooldridge, Los Angeles, California, June
1959.
Olney, J. C., ItFEAT, An Inventory Program
for Information Retrieval, II 2N -4018,
System Development Corporation, Santa Monica,
California, July 1960.

Efficiency of the Factor Derived Classification System

Even assuming that the factors are stable,
it is necessary to compare the value of a classification scheme based upon factor dimensions with
the more traditional subject classification categories. An experimental test of comparative efficiency would have to be devised using as a criterion the information retrieval effectiveness of
the two systems.
5.3 Probabilistic Indexing
Maron(2) described the concept of probabilistic indexing. As an extension of his work, it
is proposed that the factor loadings of terms be
used as probability measures for determining the
category to which the document belongs. For
example, the term "social" has a factor loading of
.11 on Factor No.2, "Social Psychology and
Community Organization,!I while the same term has a
factor loading of .42 on Factor Noo 8. "General
Psychology.!! It is suggested that if the word
!!social!! occurs as a key word in an article, that
article be given a .4 probability in !!General Psychology,1t and a .1 probability in !!Social

Summary And Conclusions

The purpose of this study was to describe and
utilize an empirically based mathematical procedure for classifying documents. An experimental
library of 618 psychological abstracts was selected and coded into machine language for computer processing. The words in these documents
were ordered according to frequency of occurrence,
and 90 index terms selected from among those words
which occurred 20 or more times. Each term was
correlated with every other term, and the resulting correlation matrix factor analyzed. Ten
factors were extracted and rotated for meaning.
These were then interpreted and the results compared with, and shown to be similar to, the existing subject classification system employed by the
American Psychological Association. The study
demonstrates the feasibility of using factor analysis as a method for determining the basic
dimensions of a classification system

Implications For Future Research

Replication

289

(4)

Thurstone, L. L., Multiple-Factor Analysis,
University of Chicago Press, Chicago,
lllinois, 1947.

291

THE STORAGE AND RETRIEVAL OF PHYSIOLOGICAL AND MEDICAL DATA
IN A MODERN HOSPITAL
Paul C. Tiffany
Aerospace Corporation
EI Segundo, California
(Formerly with System Development Corporation, Project Medic)
Abstract
As an introduction this paper considers some
of the problems in data handling in a modern hospital. Next, the needs of the users of the data
are considered. The principle area of interest
is indicated as that hospital function dealing
with the storage and retrieval of the clinical
record after the patient's hospitalization. The
types of terms used in medicine are examined and
two currently used schemes for the indexing of
diseases are described. Next a storage and retrieval system that permits the medical researcher to examine or browse through clinical records
or abstracts of the records is described. The
paper concludes with observations on the need for
applied research and system development to acquire
pilot systems for the storage and retrieval of
physiological data.
Introduction
A system studyl describing a General Medical
and Surgical Hospital of the Veterans Administration indicated that faster and higher-capacity
storage and retrieval systems--possibly camputerbased--were needed to manage technical and clinical data.
Problems of Data Handling in the Hospital
Clinical records inherently defy logical control. In addition to sheer volume, the following
are typical complications:
1.

"Summaries" of hospital stays often contain lengthy "soft" literary descriptions
that are difficult to abstract and
1!harden. 1T
Medical and surgical entries in 1!Pro_
gress Notes,tI often lack the parameters
necessary to describe many complications.

Two Assumptions Regarding the Storage and Retrieval of Clinical Data
1. If a general solution exists for storage
and retrieval problems, this general solution will
be found most readily by applying the hard practical techniques used to solve storage and retrieval
problems for particular systems.
General techniques, common characteristics,
laws of behavior, and formulae will emerge from
the solutions of the problems of different systems. In some respects, each system will be
unique, as determined by the nature of the data
to be handled and the needs of the user. The common problems will be solved by deductionj esoteric
and inductive reasoning may only serve to fog the
issues.
2. If existing concepts on automatic abstracting, indexing, pattern recognition, parsing
of sentence structure, translation from physiological language to a mathematical logical language, teaching machines, heuristic programming,
etc., are collected and ordered, a storage and retrieval system will then exist for the management
of data in the clinical record.
It is possible to assemble such a system and
it should be attempted soon. This paper will suggest a broad configuration omitting details that
only can be acquired through extensive research.
Hopefully, this description will prompt other researchers to collect, refine, and integrate existing concepts, and from thiS, evolve an effective
storage and retrieval system for medical and
physiological data.
Consideration of the Needs of
the User of Physiological Data
tlReal Time" Data Storage in the Clinical Chart
The capability of storing data in 1!real

Concrete detail may not be available for
the physician's or nurse's first encounter with the unusual situation.

Soft literary comments are considered
necessary to supplement hard parametric
values.

5·

Only detailed research for an extended
period over the range of the many diseases and almost infinite number of disease combinations will yield a pattern
of knowledge such as employed by an experienced doctor when he examines a
clinical record.

_f' . . . . .

........
v...u.ll-';;::::

.J..~

~-I-

..: ........... _ ...... _..: ............ .:J

o.O.LlJ.J..i:)

..LCI..,,;.'C.l..VC:U.

__ ..................... 1.-.. ....... -. .............. __ , ... _
a0;j.L.LI....:.L.LLU,UUU.b..Lj'

~ ___ ..

...1-1....._

..l.LUlll

vIle:::

varied hospital services (wards, clinics, laboratories, x-ray, conferences, operating rooms, etc.)
and then retrieving part or all of it when requested by users, clearly, will aid in satisfactorily caring for patients. An experiment is in
progress, conducted by a joint team of researchers
from the Veterans Administration and the System
Development Corporation of Santa Monica, to demonstrate this capability in a simulated hospital
ward environment, using an IBM 1401 with RAMAC.
The project will handle those forms found in most
hospital clinical records as suggested by the
Joint Commission on Accreditation of Hospitals.

292

INFORMATION RETRIEVAL

storage of the Clinical Record After
Hospitalization

recognize the terms and words of medicine and
physiology.

Access to records stored after the patient's
discharge is a major need (and is the main interest of this paper). According to Hut't'man 2 , the
Medical Record Library (MRL) function is to provide medical records containing sufficient data
to verify the diagnosis and treatment and document the results for all patients treated in the
hospital. These records should be readily available for:

Medicine is a science which is concerned with
the abilities of recognizing, preventing, curing,
and alleviating diseases and their causes. Surgery is considered a medical science that manually
corrects, aids deformities and defects, and repairs
injuries and is, therefore, a sub-category of this
definition of medicine.

The patient,
remember the
also, if the
rate records

as busy physicians cannot
details of all their cases;
patient is readmitted, accusave time and effort.

The hospital, to review the competency of
their staff and the results of treatment,
and to compile statistics; also, for
medico-legal purposes.

The physician, to review his cases and
consultations, and to treat patients who
do not recall previous illnesses and hospitalizations; also, for medico-legal
purposes.

Physiology is a science dealing with the functions of organs and physical parts during life. By
way of contrast, "physiology" is dynamic, and
"anatomy," static.
A cursory examination reveals the large size
of the task of developing descriptor terms for the
data encompassed by these sciences. Skeptics may
weigh "Stedman's Medical Dictionary,,4 or merely
leaf through its 1656 pages of definitions.
A Smaller Manageable Area for Examination

Medical research and teaching, since
many observations can only be made
clinically.

The Storage and Retrieval of Documents Written in
the Medical and Surgical Field
The field of medical documentation is burdened by the problem of how to store documents so
that they can be recalled readily. To solve the
problem concisely, the computer must be "taught"
the language of "physiology." Hans Selye and
Miklos Nadasdi in their book on a "Symbolic Shorthand System" discuss the possible adaption of their
system to electronic machines, and state, "Perhaps
the mechanical memories of the future will not
take this particular form, but Whatever we use,
punch-card systems, electronic machines, or any
other physical aid to classification, the first
problem is to create a Simple, mnemonic language,
which can easily be fed into such machines. "3
Although it was originally designed for processing documents on stress and endocrinology,
the "Symbolic Shorthand" technique appears to be
directly adaptable to a library system for all
types of medical documents. Consideration is
given to the possibilities of generating an abstract of the clinical record, and of generating
an index based on the abstract.
This can be compared to the techniques used at Western Reserve
for doc~~ent storage.
Some Concepts of the Size of the
Medical and Physiological Lang~age
A computer system that can communicate and
handle storage and retrieval problems using medical and physiological data must be programmed to

The immense field of medical terminology may
be bounded somewhat by selecting a subclassification of the entire science, specifically, endocrinology. Endocrinology deals with the glands and
their secretions. It is further concerned with
the movement of those glandular secretions that
pass directly into the blood or lymph. In addition, the science is interested in the activation
of cells of other parts of the body by organic substances called autacoids. An example of an autacoid is the hormone thyroxine, produced by the thyroid gland, which considerably influences growth.
Why was endocrinology selected? After
attending conferences, visiting wards, examining
the data in the charts of the patients, and discussing the question with various doctors, it appears that endocrinology involves a larger volume
of objective data than other services and would
benefit most directly from computer handling.
Much work has already been accomplished to firm
these data and,therefore, facilitate this study.
To reduce the problem to a level suitable for
this paper, one small area of the entire subject
of endocrinology was selected, namely, the Hypophysis. A study of this gland, though quite
complex, is easily bounded, and appears to afford
hard and finite data. The following material is
presented to indicate how large the terminology
and indexing problem is for a single gland.
The Hypophysis is the pituitary body. It consists of two lobes and is located at the base of
the brain in a depression of the sphenoid (wedge
shaped) bone called the pituitary fossa. The
smaller posterior lobe is developed from and attached to the brain by the infundibulum, the name
given to the stalk attachment of the hypophysis.
The larger anterior lobe is developed from the
buccal cavity, the cavity of the mouth. (See
FigJ.re l.)

THE STORAGE AND RETRIEVAL OF PHYSIOLOGICAL AND MEDICAL DATA IN A MODERN HOSPITAL

DIAGRAM OF THE HYPOPHYSIS
a. Anterior pituitary. b. Pars intermedia. c. Neural lobe. d. Pars
tuberalis. e. Mammillary body. f and g. Hypothalamic nuclei. h. Optic
chiasma. i. Tuber cinereum.
FIGURE 1

293

INFORMATION RETRIEVAL

294

The foregoing serves to introduce the wide
range of data used to describe this gland and its
functions. Hans Selye in his "Symbolic Shorthand
System," conceived of the following eight major
categories.
1. Actions upon the hypophysis. The following types of actions are viewed as interventions
upon the gland and its system:
a)

Extirpation, complete removal of the

Partial extirpation

Exposure to ionization or x-rays

gland

pathways and flow
b)

c) Metabolism of the hormones, their
fate in the body
d) Utilization of the hormones for the
performance of their functions in the body.

5. Pharmacology. This deals with the drugs
used in treating the hypophysis, and includes such
items as:
a)

d) Activation, excitation, or depression
of gland by drugs, medication, etc.
Morphology. The features, form, and
structure of the, organism are covered by the following two subjects:
2.

a)
the gland.

b)
and results

Dosage, effect data between dosage

Sensitization and desensitization

Pharmacological resistance

Immunity and allergy

Toxic effects

6. Hypophyseal Hormones. This subject deals
with the secretions of the gland:
a)

Crude hypophyseal extracts

Crude anterior lobe extracts

Adrenocortocotrophic hormone

Somotrophic hormone

Gonadotrophic hormone in general

3. Chemistry. The general chemistry of the
structure of the gland is divided into two sections.
a)

Application

c) Relationships between chemical and
pharmalogic effects

Anatomy--the structure and parts of

b) Histology--the minute structure of
the tissues. For example, the posterior lobe is
composed of neuroglia-like cells (like the brain
cells). These spindle-shaped cells are known as
pituicytes. These cells are filled with a clear
homogeneous material known as hyaline bodies,also
Hering's bodies. This smaller lobe also consists
of connective tissue, blood vessels, and numerous
nerve fibers. The larger anterior lobe consists
of cords of cells which are separated by very
small channels, microscopic vessels. There are
three types of cells in this lobe, chromophobes
which do not stain easily, acidophils which stain
with acid dyes, and basolphils which stain with
basic dyes.

Mechanism of action

Follicle stimulating hormone
Luteinizing hormone

Organic compounds of the gland

Luteotrophic hormone
f)

Thyrotrophic hormone, TSH

Crude middle lobe extracts

Melanophorotrophic hormone, inter-

Synthesis

Other middle lobe hormones

Chemical activation and inactivation

Posterior lobe extracts

Vasopressin, antidiuretic hormone

Oxytocin

Other posterior lobe hormones.

b) Chemistry of the hormones, including
such terms as:
Trade names
Extraction

medin

Preservation, etc.

Humoral Physiology. This classification
deals with the functions of the blood and lymph
ducts in relation to functions of the gland:

Mecha~is~ of secreti0~J incl~ding

More terminology must be introduced to understand the functions of SOT."le of these pituitary

THE STORAGE AND RETRIEVAL OF PHYSIOLOGICAL AND MEDICAL DATA IN A MODERN HOSPITAL

hormones. The smaller posterior lobe furnishes a
secretion that stimulates contraction of unstriped
muscular tissue; raises blood pressure; and is
oxytocic (hastens childbirth), antidiuretic (decreases the secretion and discharge of urine), and
melanophore (contrOl of skin pigmentation) dispersing. The larger anterior lobe furnishes a
gonadotrophic hormone (affecting the sex glands),
thyrotrophic hormone (affecting the development
and activity of the thyroid), and an adrenotrophic
hormone (abbreviated as ACTa, influencing the
growth and activity of the adrenal cortex); prolactin (stimulating the secretion of milk); and
generally contributes to growth promotion. Ketogenic (producing acetone bodies in the blood),
diabetogenic (causing diabetes), and insulinantagonizing effects are obtained by injection of
the extracts of this anterior lobe.

295

Hypopituitarism in general
Simmonds disease
Sheehan's syndrome
Hypophoseal dwarfism
Hypophoseal infantilism
Hyperpituitarism in general
Acromegaly
Cushing's syndrome
Pseudo Cushing's syndrome
Berardinelli's syndrome

Pathology of Hypophysis. This classification deals with the condition of the gland or
fluid produced by disease, and considers such
items as:
a)

Aplasia--the congenital absence of

Diabetes inSipidus
Antidiabetes insipidus
Inflammation of the hypophysis

an organ.
Non-endocrine hypophoseal tumors
b) Hyperplasia--the increase in tissue
elements such that the bulk of the organ is increased, excluding tumor formations.
c) Hypoplasia--the defective development of an organ.
d)

Accessory glands.

Hemorrhages and other vascular

Any other malformations.

Inflamations.

Tumors.

lesions.

Diseases of the Hypophysis. Diseases of
this gland are defined as any malady, ailment, or
maladjustment that causes a condition in which
bodily health is impaired. Classifications
include:
a) Diseases with
either lobe.

~deractive

pituitary,

b) Diseases with overactive pituitary,
either lobe.
c)

Tumors of the hypophysis.

Injuries and operations.

others.

As an examination of the broad classifications
of diseases used in a system for the storage and
retrieval of documents dealing with studies of
stress and endocrinology, the following diseases
of the hypophysis are listed:

Cranio-pharyngioma
A Look at Two Coding Schemes that are
Currently Used to Index Hospital Records
Two well developed schemes exist for classifying diseases and for assigning number codes to
identify the diseases. The classification and
coding are described for the pituitary gland. The
first system is that listed in the ICDA, "International Classification of Diseases, Adopted for
Indexing of Hospital Records."5 The second is the
SN, the "Slandard Nomenclature of Diseases and Operations, " published for the American Medical
Association.
Description of Diseases of the Hypophysis as
Listed in the ICDA
The International Classification creates a
"separate title or code number in the classification only when a separation is warranted because
of the frequency of its occurrence."5 This system is based therefore on the frequency with
which diseases occur and is a statistical model of
public health infOl"'nlation. .L.L uHe user OI tinJ.8
index requested data that occurred most frequently,
then this system might satisfy his needs. The
medical research worker, however, is not always
interested in data primarily because of its frequency of occurrence (for example the common
cold).
The ICDA states, "For hospital indexing purposes, the most efficient classification system is
one which permits the location of a maximum number
of pertinent records with the review of the least
number of records." ICDA adherence to its own definition of efficiency is covered in a study reported in the Journal of the American Association

INFORMATION RETRIEVAL

296

of Medical Librarians,7 which contrasts this indexing system with the SN.

In Appendix 1 some disease symptoms and terms
described to clarify the classifications; however, these descriptions do not appear in the International Classification. The major category
dealing with diseases of the endocrine system is
Number III: Allergic, Endocrine System, Metabolic
and Nutritional Diseases. The next lower level of
classification is Diseases of other Endocrine
Glands (270-277). Under sub-class 272 are most of
the items that are of interest to this paper. For
a more complete treatment of indexing in the ICDA
refer to Appendix 1.
O~Q

that abstracts the clinical record for indexing
and storage also abstracts the users' request. The
system compares the request with stored information and then displays the matched abstract, indirectly asking if it is what the user desired.
The user then either accepts What is offered or
modifies his request. This inter-communication
between the system and the user permits the retrieval of a single abstract, several abstracts,
a solitary clinical record, selected parts of a
record, selected parts of several clinical records,
or several complete clinical records.
The presentation that follows covers three
areas:

Description of Diseases of the Hypophysis as
Listed in the Standard Nomenclature

1. The Movement of Data in Processing of
Clinical Charts for Storage.

The technique of indexing in the SN is more
highly ordered than in the ICDA and would appear
to lend itself more readily to automatic programming.

2. The Movement of Data in Retrieving Abstracts and Charts.

In general, the plan of the SN is to code
the disease as a two part index. The first part
indicates topographically the system of the body
that is infected; the second indicates the etiology, the cause of the disease. Refer to Appendix
2 for an example of the SN applied to diseases
and operations of the hypophysis gland.
Appendices 1 and 2 suggest the complicated
thesaurus that must be considered for any data
retrieval system. A set of mliterms as advocated
by Dr. Mortimer Taube, or descriptors as promoted
by Calvin Mooers, would be extensive even for so
limited an area of the human body as the pituitary
gland. An extrapolation to the complete body and
its systems shows the enormity of the complete
storage and retrieval problem. Perhaps, retrieval systems should be specialized and deal only
With individual medical areas in the beginning.
A "Storage and Retrieval" System Description
The system illustrated in Figure 2 was
evolved by synthesizing a number of independent
concepts. Many of these concepts will require
considerable development and study before firm
operational techniques may be recommended; however, rudimentary and perhaps even somewhat crude
methods are available presently to set up a prototype system.
"In the majority of cases, the problem is
not that our existing technology is insufficiently
advanced to provide the mechanisms we need for
effective handling. In short, the practical problem we face in this area is the proper selection
and application of the systems and eqUipment now
available to us, and to do this properly we must
understand clearly the elements of our own individual working environment." S
The purpose of this proposed system is to
provide high-speed storage and retrieval for the
~ser of medical data.
The part of the syste~

3.
System.

Communications of the User with the

The Movement of Data in Processing of Clinical
Charts for Storage
This concept is illustrated in Figures 2a and
2b. Figure 2a is the legend for the flow diagram;
the flow of the data in processing the clinical
charts as they come from the ward is shown in
Figure 2b. The clinical charts (input data) are
shown entering the system at the base of the
diagram.
Read-in of Clinical Charts of Discharged
Patients to be Abstracted. Clinical charts are
entered into the system to be abstracted - (line
A of Figure 2a) by the Automatic Abstractor and
classified by the Index Classifier. In the early
stages of system development the process would be
manual; however, efforts should be extended to
computerize this function. The efforts of Zellig
S.Harris9 and others to parse the English sentence
indicate a possibility of selecting key words in
the doctor's summary of the clinical record and
automatically abstracting them. The abstracts
would be indexed according to the primary disease
as coded by the standard nomenclature with next
level storage indicated by secondary illnesses.
Further and deeper indexing should now be made by
abstracting the clinical chart. The resulting
abstract used as an index will attain a level of
storage and retrieval far beyond the capabilities
of modern medical record libraries, particularly
for research purposes. The system will also allow
for browsing by the user. An existing manual system is the Symbolic Shorthand System of Hans
Selye,3
Read-in of Clinical Charts to be Reduced.
The read-in of clinical records of discharged patients for reduction to micro-image is handled at
the same time that the clinical chart is being
abstracted and indexed. Line B indicates the
movement of the chart to the micro-image producer.
Several devices exist for this function incl'.-ld5_ng

THE STORAGE AND RETRIEVAL OF PHYSIOLOGICAL AND MEDICAL DATA IN A MODERN HOSPITAL

Magna card, Minicard, File search, "Walnut,tI Recordak, and other micro recording and display systems.
Storage of Abstract Classification and Index
for Retrieval of Abstract. Line C indicates the
movement of the coded abstract to the Request and
Abstract Index Matcher. In a study made for the
National Science Foundation, and in a course on
Information Storage and Retrieval,lO Dr. Robert M.
Hayes presented a mathematical model in which an
association matrix was used to indicate the relevancy between documents.
tlOf particular mathematical interest is the
fact that powers of the association matrix provide a method for determination of its eigenvalues and thus represent an approximation to the
methods of eigen-value analysis and factor
analysis. tI
This technique suggests that an abstracted
request can be treated as a vector and multiplied
by the association matrix some tin" times to attain
an approach to an "eigen" vector, thereby processing the original request to attain a close
fit to the stored file of documents. This matching technique affords the requester considerable
freedom in forming his request, using key words
as a basis. A researcher could draw as many relevant cases from the stored data as he desired in
either direction in the file from the closest
match.
Storage of Abstract in Appropriate Classification as Determined by Automatic Abstraction.
Line C leads to a storage of abstracts. The first
level of classification or index is made by use of
the SN number of the primary diagnosis, and then
by the SN number of the secondary diagnosis. The
next level would be stored as the coded abstract
itself, possibly as a dynamic file of tlagentstl
acting on tltargets tl • Associated with each filed
abstract would be a stored serial index to retrieve in part or completely the clinical charts
of interest.
Transfer to Storage of Complete Charts. Line
E indicates the movement of the micro-miniaturized
data into storage. This storage is arranged as a
serial file, with the most recent information
most accessible. The file would be culled constantly, and charts grouped by admission dates. A
serial number assigned to a patient would be preserved for that patient; permittin~ grouping all
his hospital stays under his most recent admission.
Movement of Data in Retrieving Abstracts and Charts
The following flow of data is presented to
indicate how the system retrieves data for the
user.
Read-in of Text of Request. The input of
the user is indicated by line 1 (Figure 2b), and
represents "n" possible iterations of user requests as he modifies them to retrieve the clinical data he wants.

297

Request Index as Generated. Line 2 indicates
the movement of the generated request index. This
index is to be developed by the same abstracting
technique (key words) as used on the clinical
charts.
tiThe inquirer's document would then be coded
in exactly the same manner as the documents of the
collection have been encoded, and the resulting
notional abstract would be set up as a question
pattern in a data-processing machine of adequate
functional ability."ll
As described previously, a correlation matrix
could be used to obtain the chart with the closest
match to the generated request.
Temporary Storage of Request Index. Line 3
shows the movement of the index with the closest
match into a storage register that will hold the
data, pending an examination of the matched abstract by the user of the system.
Abstract Index with Closest Match to Request
Index. The abstract is now moved via line 4 to a
device that will print out, or display by same
other technique (such as a cathode ray tube), the
matching abstract, for the user's examination.
The diagram indicates "ntl possible feedbacks to
the user/researcher until he is satisl'ied that the
abstract contains the material that he desires.
This feedback technique is similar to automated
teaching practices and permits communication between the system and the.user.
Activation Switch Indicating Agreement of
Requestor with Match. Line 5 carries the input
of the user indicating his satisfaction with the
matched abstract. By switch insertion the user
will modify his request ,e.g. ,requests for the
quantity of abstracts desired. Related abstracts
will be stored near the matched abstract.
Index Used to Activate Output of Abstracts.
The indication of acceptance of the match will
move the index, illustrated on line 6, to activate
the output of the abstracts from storage as per
the user's request.
Output of Abstracts. The abstracts requested
will now be produced, probably via on-line printer,
for the user, as indicated by line 7. Each abstract, as described previously, will carry a
s-erial index as part of the data. to enable

retrieval of clinical charts, if desired.
Entry of Request Using Hospital Serial Number. At this point, by examining the abstracts
the user will determine which clinical records or
forms or parts of records he desires. For example, the researcher may only be interested in
the laboratory reports, or the medications used
for a certain classification of diseases. Selectively USing the serial indices and guides to
specific parts of the charts the user inserts a
request (as illustrated by line 8).

r---'----------------------------------.-------------------------n------------------------'
COMMUNICATIONS OF THE USER WITH THE

SYSTEM

t5
00

Writte n reque sts for retrieval of clinical data stored in discharged patients' charts.
Image of abstract data with closest match to request for examination by requestor.
Activation switches to retrieve abstracts in classification which agrees with request.
Printout of abstracts of clinical records in classification that matches request.
Keyboard for insertion of serial number to request whole or that part of clinical record which is desired"
Insertion will also indicate method of output.

@
@

Display output of selected parts of data as indicated in retrieval request.
Hard copy output of selected clinical data on printer.
MOVEMENT OF DATA IN PROCESSING OF CLINICAL CHARTS FOR STORAGE

Read-in of clinical records of discharged patients to be abstracted.

®
©

Read- in of clinical records of discharged patients to be reduced to micro images.
Storage of abstract classification and index for retrieval of abstract.

Storage of abstract in appropriate classification as determined by automatic abstraction.

Transfer to storage of complete charts.
Data are now micro- miniaturized.
MOVEME~NT

CD
®

Charts are now stored in agreement with hospital serial index.

OF DATA IN RETRlEVING ABSTRACTS AND CHARTS

Read-in of text of request describing the type and number of clinical charts desired to be retrieved.
Request index as generated by automatic abstractor.

Temporary storage of index generated for this request.

@)
@)

Abstract index with closest match to request index.

Index used to activate output of abstracts in this classification for examination.

Output of abstracts with hospital serial number to be used to retrieve charts as desired.

Entry of request using hospital serial number for retrieval of complete records or parts of charts as
desired.

Output of charts or selected parts as requested.

Activation switch indicating agreement of requestor with match.

z
"'%j

FlGURE 2a.
LEGEND FOR INFORMATION STORAGE AND
RE TRIEVAL SYSTEM SHOWN IN FIGURE 2b

o
~
a::
>,..,
5

z
~
t%j
,..,
~
;;
~

t"'"

t-3

:::t:
~

fJ.J

USER/RESEARCHER

ztj

~
~

t-3

t""'

o~
"'d

Written Requests.

Keyboard
Retrieve by
Serial Number

Data Needed For
· Research
· Legal
· Accreditation

Record
Printouts
Clinical Charts

:::t:
>-<:

fJ.J

o
t""'

o
o

o;>
t""'
;>

....-I

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'8 1

'01

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I,.,

I
iii

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Q)
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1
'8
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.-4

[

o
Index of
Classifications

Reque st and
Abstract
Index Matcher

;>
t""'

Miero Image Storage
of Complete
Clinical Charts

52
;>

s:o
tj

Automatic Abstractor
and
Index Classifier

____

~.-

•

lD~

~
~

Abstract with Serial Hospital Admissions
Number, Stored According to
Index Classification of Medical Record

______________________

Clinical Records From Wards I
After Discharge of Patient

:::t:

fJ.J

Micro Image
Producer

~
t""'

FIGURE 2b.
INFORM:ATION STORAGE
AND RETRIEVAL SYSTEM
FOR CLINICAL RECORDS

INFORMATION RETRIEVAL

300

Output. The output as indicated by line 9
can be of two types: a display of individual bits
of data for visual examination, such as a display
of the doctor's orders which had been given for a
patientj or a printout of partial or complete
clinical records that had been stored as micro
images.
Communicating with the System
This section briefly describes the inputs
(requests) from the user and outputs (retrieved
data) to the user.

Display Output. The system can display a
visual-type image of individual pages of the clinical chart (Output VI). This capability will enable the research worker to examine a part of a
clinical chart directly if the data in the abstract were insufficiently detailed.
Hard Copy Output. The printed output (VII)
supplies the user with a "hard copy" of the retrieved clinical chart, or section of the chart
exactly as it Was stored when transmitted from
the ward.
Conclusion

Written Requests. For retrieval of the data
stored in the clinical charts of discharged patients, the user will write (typewrite) an input
(I) to the system using an SN number and a written
description of his request. The request may be
dictated by various requirements such as the need
of data to defend the hospital against malpractice
suits, the retrieval of records for statistics to
support research endeavors, the gathering of
figures for hospital management to compile accreditation reports, etc.
Image of Abstract Data with Closest Match.
This output (II) from the system makes it possible
for the researcher to see the abstract that is
the closest match to his request. If the abstract
does not meet the needs of the requestor, he can
reframe his request and the system will display a
new matched abstract.
Activation Switches. This input (III) provides the requestor with the capability of retrieving as many abstracts as he may wish to look
at. These abstracts are stored in the immediate
environment of the abstract that best fit the
user's request. This satisfies two needs of the
user: the desire to browse through the file, and
the need to retrieve a quantity of abstracts to
obtain additional material to support research
and teaching projects. By switch insertion the
user will indicate to the system how much material
he Wishes to examine, and what type of output
(soft visual-display or hard printed-copy) he
desires.
Printout of Abstracts. The retrieval system
will supply the output (IV) in the form of a
printout of the abstracts the user requested. The
storage location of the abstracts has been supplied
by the matching techniques and the storage plan.
No provision would be made to exceed the boundaries of the SN classification in supplying the
quantity of abstracts desired.
Keyboard. After examlnlng the abstracts and
deciding that the complete clinical charts or
parts of the charts are necessary, the requestor
will key into the system the serial number in the
abstract, the format number for the part or complete clinical record, and the method of output
desired. This input (V) directly addresses the
micrO-image storage system and provides by
switch-insertion the serial index to retrieve the
!'eguired. data.

Economic considerations of this system configuration appear quite extensive; however, this
configuration is suggested for the purpose of
demonstrating and developing the feasibility of
such systems. Simplification of functions and
equipment should lead to practical operational
concepts.
The level of retrieval for research, the
rapidly expanding field of medical knowledge, the
mounting heap of clinical charts in hospital stor=
age vaults, and the increasing demands upon the
hospitals because of our rapidly growing population indicate a need for increased research and
development on storage and retrieval systems.
This paper concludes with a series of observations drawn from the "Proceedings of the San
Jose Conference on Health Information Retrieval,

1959. "12
"1. Health and medical information is the
essential requisite for effective care of individual patients and one of the essential needs
for sound research but its volume and complexity
has become so great that it can no longer be
effectively stored, codified, retrieved and transmitted by conventional methods.
"2. The problems and needs of health informatiou :ceLl'.:Leval are of cl'itical iiupo:rtance to all
professional disciplines related to health, to all
agencies concerned with health, rehabilitation,
welfare and correction. These problems and needs
are nation-wide in scope.

"3. The technology of information storage
and retrieval is already in a state of development where it may be applied to this problem.
"4. To accomplish this objective, intensive
studies are necessary in order to define precisely
the information retrieval requirements of health
and medical practice and research.

"5. The benefits to the individual and
social health of man to be derived by successfully
doing so are considered to be very great and it is
therefore recommended by the conference that the
development of definitive studies directed toward
solution of this problem be encouraged by every
means possible."

THE STORAGE AND RETRIEVAL OF PHYSIOLOGICAL AND MEDICAL DATA IN A MODERN HOSPITAL

301

Appendix 1
The ICDA Index
The following listing is in the format of the
ICDA. Comments and descriptions not a part of the
ICDA are placed in parentheses.

Z72.

DISEASES OF PITUITARY GLAND

Z72.0 Anterior pituitary hyperfunction
(The diseases in this general group
are due to over-activity of the anterior lobe of the hypophysis.)
Includes: Acromegaly (also known
as Marie's disease. This disease
has the following symptons: enlargement of head and face, hands
and feet, and thorax. This growth
is due to excessive secretion of
the acidophil cells of the anterior
lobe. )
hyperpituitarism (A condition, which is marked by acromegaly as described above and hypertrichosis, which is the abnormal
growth of hair such as on the face
of women or on the back in both men
and women.)

Now the listing proceeds with the
next classification of pituitary
diseases.)
Z72.l

Anterior pituitary hypofunction
(Hypofunction is the opposite of
hyperfunction. Instead of overactive the anterior lobe is underactive. )
Includes: adiposogenital distrophy
(This is a disease of the type of
Froehlich's syndrome. The condition
is caused by a deficiency of the anterior lobe and often combined with
a deficiency of the posterior lobe.
Symptoms of the disease are: increase in fat, loss of sexual power,
atrophy of the external genitals,
and loss of hair.)
dwarfism
(of several types)
-hypophyseal
Loraine type

hypophyseal gigantism
(Idiopathic infantilism)
premature puberty
pituitary
(At this point, the ICDA, to prevent hospital personnel from making mistakes when
using this coding index, lists three diseases that should not be listed under
272.0.)

Froehlich's syndrome
hypopituitarism
(juvenile)

Excludes:

Basiophilic adenoma

(Z77.0)
Cushing's syndrome

pituitary
cachexia

(Z77.0)
dwarfism
pituitary basophilism

(Z77.0)
(To show how much is excluded; a
description of Cushing's syndrome
in Stedman's Medical Dictionary
lists the folloWing group of symptoms for these diseases: abnormal
carbohydrate metabolism; obesity of
head, neck, and trunk; decalcification of the bones; and increased
blood pressure. It has been suggested that the syndrome points to
the presence of a basophil adenoma
of the hypophysis cerebri, pituitary
basophilia. This describes a pituitary tumor made up of basophil cells.

infantilism
obesity
Simond's disease
(This disease is marked by premature
aging, rapid atrophy of the genital
organs with repression of secondary
sexual characteristics, and loss of
hair. Disease is usually noted in
young women due to atrophy or diminished functioning of hypophysis.)
(Again to prevent errors the ICDA advises
against the inclusion of the following
diseases.)

302

INFORMATION RETRIEVAL

Excludes:

195.

dwarfism:

MALIGNANT NEOPLASM OF OTHER ENDOCRINE
GLANDS

achondroplastic

195.3 Pituitary gland and craniopharyngeal

(758.0)

duct (pouch)
(occasioned before
birth)
congenital
Nffi

Includes:

(277.0)

malignant craniopharyngioma,
craniobuccal (Rathke's)
pouch

(277.1)
hypophysis cerebri

pancreatic

(587.9)

224.

BENIGN NEOPLASM OF ENDOCRINE GLANDS

dwarfism and infantilism

224.2 Pituitary gland and craniopharyngeal

(277.1)

duct (pouch)
infantilism NOS

(277.9)
Includes: tunor unspecified whether
benign or malignant

(Then the ICDA goes on to the next
listing.)

(Again in the section on OPERATIONS AND

272.2 Chromophobe adenoma, pituitary

TREATMENTS the following classification is
found. )

(A tumor in the chromophobe cells
of the anterior lobe.)

OPERATIONS ON ENDOCRINE SYSTEM

(08-09)

272.9 other and Unspecified
OPERATIONS ON OTHER ENDOCRINE GLANDS
Includes:

abcess

09.2

Hypophysectomy (pituitectomy)

adenoma Nffi (tumor)
Includes:

complete

partial

excision
of pituitary

trans frontal

neoplasm

transphenoidal

cyst
diabetes insipidus
(A disease characterized by the excretion of large amounts of pale
urine of low specific gravity, and
caused by a deficiency in the antidiuretic action of the gland.)

09.3

other Operations on pituitary gland
Includes:

Dyspituitarism
(A cCr:lplex of symptoms due to eithf'!1"
excessive or deficient pituitary
action.)

aspiration or
drainage

biopsy

craniobuccal
pouch

incision and
drainage

eosinophilic adenoma
(A tumor of the chromaphil cells of
the anterior lobe associated with
gigantism and acromegaly.)
(This concludes diseases of the pituitary in
the ICDA, however, to be complete,classification
277 must also be considered.)

277.0 Pituitary basophilism
Includes:

basophilic adenoma
Cushing's syndrome

(also under major classification II dealing
with neoplasms the ICDA lists data of importance.)

Rathke's
pouch

THE STORAGE AND RETRIEVAL OF PHYSIOLOGICAL AND MEDICAL DATA IN A MODERN HOSPITAL

303

Appendix 2
The SN Index
The material below will illustrate the coding
of the SN by showing how it is applied to coding
diseases and operations of the hypophysis. Figure
3 shows the word structure of this index. The
broadest classifications are made topographically
by systems of the body. System 8 is the class
dealing with the Endocrine system. The Endocrine
system classification is divided into 9 categories,
each coded by a two-digit number as follows:

- 6 Diseases Due to or ConSisting of Static
Mechanical Abnormality

- 7 Diseases Due to Disorder of Metabolism,
Growth or Nutrition

- 8 New Growths
- 9 Diseases Due to Unknown or Uncertain
Cause with the Structural Reaction
Manifest

80 Endocrine System
81 Thyroid Gland
82 Parathyroid Glands
83 Thymus Gland

- X Diseases Due to Unknown or Uncertain
Cause with the Functional Reaction
Alone Manifest
- Y Diseases Due to Cause not Determinable
in the Particular Case.

84 Pituitary Gland
85 Pineal Gland
86 Adrenal Glands
87 Pancreas

As this paper is more interested in the plan
and logic of the classification than the entire
list of diseases, all diseases are not presented;
however, as most troubles of the pituitary gland
are due to over and under activity an examination
of the scheme of - 7, Disorder of Metabolism, is
presented.

88 Gonads

- 77 and - 78 Disturbances of Specific
89 Carotid Gland
Classification 84, the Pituitary Gland, has
6 subdivisions coded as follows:

840

Pituitary gland, generally

Endocrine Organs or Hormones

-776 Pituitary gland, anterior lobe, increased or perverted function

-777 Pituitary gland, anterior lobe, decreased function

841 Anterior lobe
842 Posterior lobe
843 Pars intermedia

-778 Pituitary gland, posterior lobe, increased or perverted function

-779

Pituitary gland, posterior lobe, decreased function.

844 Pituitary stalk
845 Craniobuccal (Rathke's) pouch
Subse~uent digits, separated from the topographical classification by a dash, define the
etiological classification (the causes of the
disease). The first digit after the dash indicates the cause. For example, in the case of the
pituitary gland, the causes are listed as follows:

By this scheme, the classification of diseases
due to metabolic disturbance is as follows:

Diseases due to Disorder of Metabolism,
Growth or Nutrition

841 - 776 Anterior pituitary hyperfunction
841 - 7761 HYPophyseal gigantism

- 0

Diseases Due to Prenatal Influence

841 - 7762 Acromegaly

- 1

Diseases Due to Infection with Lower
Organism

841 - 7763 Pituitary basophilism

841 - 7764 Premature puberty
4 Diseases Due to Trauma or Physical
Agent

-50 Diseases Due to Circulatory Disturbance

841 - 777 Anterior pituitary hypofunction
841 - 7771 Pituitary dwarfism
841 - 7772 Juvenile HYPopituitarism

304

INFORMATION RETRIEVAL

ETIOLOGIC
CLASSIFICA TION
Cause of Disease

TOPOG RAPHIC
CLASSIFICA TION
Site of Disease

"CHROMOPHOBE CARCINOMA OF PITUITARY GLAND"
For Diseases of Hypophysis

Site of Operation

Operation

"HYPOPHYSE CTOMYi!

For Operations on Hypophysis

FIGURE 3.
EXAMPLE OF STRUCTURE OF WORD CODES

THE STORAGE AND RETRIEVAL OF PHYSIOLOGICAL AND MEDICAL DATA IN A MODERN HOSPITAL

841 - 7773

Hypopituitary cachexia

841 - 7774

Sex infantilism

841 - 7775

Sex infantilism with
obesity

841 - 7776

Dwarfism and infantilism

842-779

References
1

MEDIC Branch--Special Development Division of
SDC. Patient Data ProceSSing in the Hospital-System Description, TM(L) 566/001/00, Jan. 1,
1961.

HUFFMAN, EDNA K., R.R.L. Manual for Medical
Record Librarians, Physicians Record Co., fourth
edition, 1955.

SELYE, HANS and MIKLCB NADASDI. Symbolic Shorthand System for Physiology and Medicine, ACTA Inc., Montreal, second edition, 1958.

TAYLOR, NORMAN BURKE, V.D o, M.D. (ed.). Stedman's Medical Dictionary, The Williams & Wilkins
Company, 1957.

International Classification of Diseases Adapted
for Indexing of Hospital Records and Operation
Classification, U.S. Department of Health, Education, and Welfare, Public Health Service, December 1959.

PLUNKETr, RICHARD J 0, M. D. (ed.) and ADALINE C.
HAYDEN, R.RoL. (assoc. ed.). Standard Nomenclature of Diseases and Operations, The American
Medical Association, McGraw-Hill Book Company,
Inc., 1952.

"Efficiency in Hospital Indexing of the Coding
Systems of the International Statistical Classification and the Standard Nomenclature of Diseases and Operations, II Journal of the American
Association of Medical Librarians, Vol. 30, No.
3, Part 1, June 1959, pp. 95-111, 129.

~,ROBERT

S. "Specialized Planning for Information Retrieval--Modern Trends in Documentation," Symposium, University of Southern California, edited by Dr. Martha Boaz, Pergamow
Press Ltd., April 1958

HARRIS, ZELLIG I. "Transformations and Discourse Analysis Project," Department of Linguistics, UniverSity of Pennsylvania.

Diabetes insipidus due to unknown
cause

Under the classification - 8 for NEW GROWTHS
a letter, A through I, may be added to specify the
Malignancy Code for the growth.
"A"

Benign - no premalignant significance

305

For example:
841 - 809lA Adenoma of pituitary gland
Coding for Operations. For coding surgery
)f the pituitary gland, the following plan is
lsed. See Figure 3.
- 0

8 .. - 01

- 1

Incision (to cut open)
Exploration of endocrine gland
(The periods .• are to be filledin with digits to indicate the
site. For example 841 - 01 is
an exploration of the anterior
lobe. )
Excision (to open and remove,
cutout)

820 - 1.

Parathyroidectomy

830 - 1.

Thymectomy

84. - 1.

Hypophysectomy (The first
period is to be filled-in to
indicate the site. For example, 842 - 1. is the removal of the posterior lobe.)

850 - 1.

Pinealectomy

860 - 1.

Adrenalectomy (The final
period is to be filled-in
with a 2 or 3 to indicate
complete or partial. For example, 841 - 13 is the partial
removal of the anterior lobe.)

811 - 11

Local excision of lesion of
endocrine gland (Periods are
replaced by digits to indicate
the exact part of the hypophysis.)

811 - 16

Biopsy of endocrine gland

10 HAYES, DR. ROBERT M. "Information Storage and
Retrieval" (x459CD), U.C.L.A., October 1961.
11 LUHN, H. P. "A St.atistical Approach to Mechanized
Encoding and Searching of Literary Information,"
I.B.M. Journal of Research and Develonment. Vol.
1, No. 4, October 1961.
•
-~. -12 Proceedings of the San Jose Conference on Health
Information Retrieval, 1959.

307

FACT SEGMENTATION
Martin N. Greenfield
Minneapolis-Honeywell EDP Division
Wellesley Hills, Massachusetts

The FACT Compiler is Hone~Nell's English
narrative compiler used for co~uereial
data processing applications. The program
segments created by FACT have their position in
memory dynamically relocated in order to make
the most efficient use of the available core
storage. The methods employed in this operation
will be described as they are general in scope
and of sufficient merit to find use in other
applications.
lan~~age

Inter segment communication is more inVOlved
because the positions of the segments are not
predetermined.

Segmentation is the process of dividing a
single program into pieces. This is done to
permit the operation of programs that are too
large to completely fit into memory. The pieces
of the program are loaded only when needed. By
having these segments time share areas of memory,
the program may be executed.

Despite these penalties, the FACT Compiler
design uses dynamic allocation for its object
program segmentation primarily because it is
so much more flexible and economi~al in its use
of space. Applications such as data processing
and information retrieVal are characterized by
handling large volumes of input having widely
varying processing requirements. It is generally
not known at the time a program is generated what
the mix of processing segments and storage areas
should be during each period of progra.'ll execution.
These requirements are dependent on the input.
Only a data sensitive segmentation control can
precisely determine what minimum portions of a
routine must be present. Static allocation must
compensate for this by keeping segments present
for the worst case. The more flexible dyna.'llic
allocation conserves space by reacting only as
needed. Segments that are unneeded are not kept
in memory. Segments are loaded into what space
is available at the time they are entered rather
than requiring a specific area be designated for
them. Because of this conservation of space,
object code placing emphasis on execution speed
at the expense of memory may be generated.

Segmentation

The importance of segmentation has grown
with the size of programs being produced. This
has been accentuated by the popularity of compiler
usage. It has become easier and as a result
practical to write larger programs attacking
larger problems. Divorcing the compiler user from
machine considerations tends to have him create
larger programs. The com~iler tends to generate
code that is more general and requires more space
than the human created codes. The result is that
every major compiler must give carefUL consideration to segmentation provisions.
Static and Dynamic Allocation
The customary practice of assigning memory
in segmentation operations is static allocation.
At compilation, assembly, or scheduling time,
the area available to each segment is determined.
The space is assigned and the segment always
occupies the same locations whenever it is loaded.
During execution, the flow of the program determines when each segment is lOaded.
More recent developments have led to the
usage of dynamic allocation of segments. At
execution time both when a segment is to be
loaded and where it is to go is determined.
Allocation is determined by the monitor ~d can
vary for subsequent loadings of the same segment.
Dynamic allocation requires a much more
conplicated loading and control routine than its
static coun~erpart. More time is required to
lo~d a segment because it must have its contents
conditioned to the positions it is to occupy.

Characteristics of FACT Segmentation
Generally segments are composed of all of
the instructions, constants and data storage
required for their execution. In order to take
the fullest advantage of the dyna~ic control,
FACT segments are subdivided into smaller units.
The smaller the unit, the greater can be the
control over what must be present in memory.
Each major procedure, input edit procedure,
report procedure, or internal or external file
area is a segment. The advantage in separating
segments from their file areas can best be
clarified by example. A procedure may be
operating on File A and File B. Upon terminating
the operations on File B, the space used by File
B may be made available to some other segment
while operations continue on File A.
The mix of segments present during any period
of execution is dictated by the flow of the
program and is in turn sensitive to the processing
requirements of the input. The storage occupied
by a segment is released as soon as it is no
longer required and this storage becomes available
to any other segment.

308

Customarily, reloading a segment requires
that it always be obtained from the secondary
storage (program tape, disc, drum). In FACT,
a check is made to determine whether a called
segment that has been released is still intact
in memory. This allows the operation to tend
to release segments as soon as possible. If
they are required a short time thereafter, they
may be activated quickly without paTlng for a
secondary storage access. Coupled with this
feature is the tendency built into the control
of keeping released segments intact as long as
possible.
FACT segments are generated as re~ocatable
blocks of code. Every segment must be operated
on at the time it is loaded to make it executable.
The location into which a segment is loaded is
determined at the moment it is to be loaded.
This location depends on the available configuration of space a~d will be described in more
detail. Each segment is relocatab1e within
memory. Segments are frequently moved and
rearranged in memory in order to accomodate the
loading of other segments.
The Segmenter
The routine that controls the segmentation
operations is called the Segmenter. It is the
initial segment of each program. It operates
with either the Honeywell production monitor
(Executive System) or checkout monitor (Program
Test System) in activating, loadin~releasing
~~d relocating segments.
The Segmenter uses two tables. The Segment
Control Table has an entry for each segment
indicating its size, its base location (current
address of the first word of the segment), its
status, and its follower. The status can be
active (A), inactive but intact in core (I),
or out of core (0). The follower is the number
of the adjacent segment in higher addressed core.
The Bank Control Table has an entry for
each memory module (2048 words). The e~try
indicates the first and last segment numbers in
the bank, the currently available inactive
storage, the highest and lowest locations
schedUled for usage in this bank, and the lowest
location that has never been loaded. The highest
and lowest scheduled locations are carried
because the Honeywell 800 has multiprogramming
capability. A scheduler defines the areas of
memory available to each program. A FACT program
must be scheduled for a consecutive set of
registers. Other programs may be in parallel
operation in the same bank but outside the
schedUled area for the FACT program. Figure 1
shows both the Segment Control Table and the
Bank Control Table.
The Segmenter normally relocates within the
confines of a bank. No Segment is located such
that it occupies portions of two b3.1'1.ks. Because

PROGRAMMING AND CODING

FACT segments tend to be small, this is not a
restriction.
Segmenter Operation
By example using figures 1-6, typical
Segmenter operations will be described.
Each FACT program initially loads the
Segmenter as its first segment. After initialization, the first segment actUally generated from
source code is loaded. When other segments are
addressed, the Segmenter will control their entry.
Segments no longer needed will be released or
deactivated by the Segmenter.
Following a short execution period, a typical
memory layout and the corresponding tables in the
Segmenter are pictured in Figure 1. The Executive
System Monitor and the Segmenter are in bank O.
Active segments 3 a~d ~ are in b~n~ one. Segments
1 and 6 in bank 0 and segment 8 in bank 1 were
loaded and subsequently released. They are in 3.1'1.
inactive status as indicated by the crosshatching.

Examining the Segment Control Table entry
for segment 5 shows that it starts in bank 1,
location 200. It is 600 registers long, is in
active status (A), and is followed in core by
segment 8. The Bank Control Table shows that
segment 0 (the Segmenter segment) is the first
and segment 6 is the last segment in bank O.
An area from bank 0 location 500 to bank 1,
location 1799 has been scheduled for this program.
1000 registers of inactive storage are available
in bank O. Location 1800 is the lowest location
in bank 0 that has never had a segment loaded
into it.
Activate Inactive Segment (Figure 2)
At this point if segment 1 is addressed,
the Segmenter will discover from the Segment
Control Table that is is intact in core. Segment 1
status is changed to active and the available
storage in bank 0 is reduced by its length.
Since this process is rapid and required no
accessing secondary storage, it is attractive to
release segments as soon as possible knowing that
they may be reactivated rapidly.
Load Segments into Unused Storage (Figure 3)
When segments 9 and 10 are addressed, they
must be loaded from secondary storage. The
Segmenter will load them into areas of unused
storage if possible so as to avoid destroying
inactive segments. Preserving inactive segments
will save accesses to secondary storage should
they be required again. Adding the segment
length and the field in the Bank Control Table
designating the lowest location unloaded permits
the Segmenter to determine that segments 9 and 10
will not fit into the end of bank 0, but will
fit into the end of bar~~ 1. The loader in the

309

FACT SEGMENTATION

monitor wil1 search for the segments and load them
where the Segmenter has specified. The Segmenter
tables are then updated (base, status and follower
fields of segments, last segment, unused storage,
lowest ~ocation unloaded of bank 1).
Release Segment (Figure

Releasing segment 5 has the Segmenter change
the segment's status and add its length to the
available inactive storage in the Bank Control
Table. Segment 5 is still intact and may be
reactivated easily if required again.
Load Segment into Opening (Figure 5)
Scanning the Ba11.k Control Tab~e will indicate
that segment 7 will not fit at the end of any
bank, but can fit into the inactive storage of
bank 1. There is no inactive contiguous storage
large enough to contain segment 7. The Segmenter
must COllect an adequate area by relocating the
active segments in bank 1.
The re~ocetion process can best be visualized
by picturing the active segments in bank 1 as
loosely strung beads. The gaps of string between
the beads represent the inactive storage. The
bead folloWing the bead at the beginning of the
b~~ is moved adjacent to it.
The gap created
below the moved bead is examined to see if the
called segment wi~l fit. If it will not, another
bead is moved adjacent to the moved bead unti~ an
adequate gap is developed. The cal~ed segment
will then be loaded into the gap.
To perform this operation it is necessary to
know the sequence of segments in the bank. This
is found starting with the first segment as
indicated in the Bank Control Table (segment 3).
In each Segment Control Word, the segment number
that follows is shown in the follower field. Thus,
segment 3's follower is segment 5, 5's fol1ower is
8 and so forth. (This refers to the segment
control table indicated in figure 4).
Scanning down the chain of segments, the last
of the first group of active segments can be found.
This s~gment is the head bead of the ana~ogy,
(segment 3)
Following it will be a group of
inactive s~gments (5 and 8). The bead to be
first moved is the first active segment (segment
9) following the group of inactive segments .
Segment 9 is moved next to segment 3. By doing
this, inactive segment 5 is overlaid~ Since
segment 5 can no longer be directly activated,
its status is changed to out of core (0). Segment
10 will also have to be moved before segment 7
will fit. After this, segment 7 is loaded into
the bank. Segment 7 will overlay segment 8, so
it is necessary to change segment 8's status to
out of core (0).
All of the above operation seems to be quite
involved and yet its operation is barely perceptible when watching it at the H-~OO console.

Squishing (Figure 6)
Segmenter operations described so far have
been confined to action within one bank. Should
a segment be called that is larger than the
inactive stnrage in anyone bank, the inactive
storage in all of the banks is accumulated in
an attempt to fit the segment. To do this,
the Segmenter emp~oys a subroutine called the
Squisher. This routine, whose name sounds
like a fugitive from a science fiction movie,
will coagulate the active segments into the.lower
addressed banks and locations available to the
program. Where necessary segments will cross
into other banks. Like all reputable science
fiction creatures, the Souisher is destructive
in that it destroys all of the inactive segments
in memory. In return it collects all of the
inactive space together into upper memory. This
should enable the loading of the called segment
that otherwise could not have fit.
Another use of the Squisher is in preparation
for executing a sort. Sorts are amorphous
by nature and operate faster if given more space.
The Squisher operation gathers all available
inactive space for the sort and informs the
sort generator of the amount of space available.
Relocation, Communication, Linkage
The explanation thus far has been about
when and why segments are relocated. The
next sections will explain how the relocation
is performed, how the migrant segments can
successfully communicate with each other, and
what the linkage is that brings the Segmenter
into action.
Relocation
The execution of any code is sensitive to
its location in storage. When segments are
moved or loaded, their code must be adjusted
to the new environment. When loading a
routine from a secondary storage as tape,
it is possible to have information on how to
relocate each word delivered to the loader.
This relocation information is used during
loading and does not permanently reside in memory.
Unavailability of relocation information for
the memory to memory relocation of FACT requires
another method of determining the relocation
rUles.
A Segment is generated as a block of code
that must be moved together. When a segment is
moved, the incremental address is the same for
every word in the segment. The segments are
constructed in the structured format shown in
Figure 8. Each word of the segment that
fOllows the same relocation rules is assembled
into the same region. One word in the segment
defines the length of each of these regions.
It then becomes possible to have a relocation

310

routine operate on each of the regions and make
the appropriate modifications.
Each segment is kept on the program tape
though it were to be loaded into Locations
starting at zero. rne relocation increment for
a program being loaded is the intiaL loading
address (or base). The memory to memory
relocation subroutine is used to perform the
relocation. Relocation data need not be kept
on the program tape nor must the loader be
concerned with this process.
Intersegment Communication
Segments must be able to operate on
information in other segments, transfer information between segments, and transfer controL
to other segments. The mobility of F~CT
segments requires a communication device
for these functions. This centers about a
table Called a Reference Region that is part
of each segment.
The Reference Region is a table of addresses
of locations in other segments that are addressed
by the segment. These entries contain initially
the number of the segment in one fieLd and the
Location relative to address zero within that
segment that is being addressed in another field.
Whenever a segment is ~oaded or moved in memory,
its relocation increment is used to update the
Refer·~nce Region tables of all other segments
of that program that are in memory. Whenever
a segment is Loaded, its Reference Region
table is updated to reflect the positions of
those segments that it addresses that are in
memory. It is possible to rapidly scan and
update the Reference Region tables by using
the Segment Control Table. The segments may
freely communicate using the information kept
current in their Reference Regions.

PROGRAMMING AND CODING

Calls to the Segmenter to release a segment
occur at points in the code that can be defined
a compilation time. The calling linkage is a
simple direct entry simiLar to those used in
entering monitors.
Linkage to activate or load a segment are
quite different. The system is designed to
allow segments to easily address each other
and at the same time have the segments
activated and reLeased frequently. It would
be most inefficient in time and storage if each
instance of intersegment addressing had to
require testing to determine whether the
segment was active in memory.
The method employed relies on the fact that
inter segment communication always uses indirect
or index addressL~g that employs the words in
the Reference Region table to load these
special registers. Whenever a segment is
inactive, all Reference Region words pertaining
to it are forced to bad parity. ~ben a segment
loads the special register with the Reference
Region word, the Honeywell 800 forces an
automatic unprogrammed transfer of controL to
a specit'ied location. The Location transferred
to is the start of the Linkage to enter the
Segmenter.
The hardware is such that no sequence
counter or any other settings are disturbed
by the unprogrammed transfer. After the
Segmenter operation, it becomes very easy to
restore control to the calling segment as
none of its settings have been changed by the
linkage. Thus, a hardware feature of the
Honeywell 800 is used as an automatic test
sensitive to the absence of an addressed
segmant.

The updatings of the Reference Region of
s'3gment 3 of the example used before is shown
in Figure 7. Addressing between segments is
always done using either indexed or indirect
addressing features of the Honeywell Boo. The
entries in the Reference Region are arranged
so they may be loaded into the special registers
for this mode of addressing.

Since a hardware error detection feature
is being used in this linkage, the Segmenter
must verify that this is a legitimate call and
not a machine malfunction. The Segmenter
reduces the probabiLity of a mistaken call
by verifying that the Location of the word of
bad parity resides in a Reference Region table
and the Segment number referred to is inactive.
The re~iabi~ity of the H-Boo memory further
reduces the probabiLity.

Linkage to the Segmenter

Operation with the Monitors

The Segmenter is dormant until called to
load, ~ctivate, or release segments. When the
Segmenter is active, the program it controls is
~ept dormant.
(This need not be the case
because of the parallel processing capabiLity
of the Honeywe~l 800). Other programs running
in parallel do keep operating. It is necessary
to stop the operation of the program calling the
Segmenter because some of its segments in memory
may be relocated, a segment may have to be loaded
from secondary storage, and other caLls to the
Segmenter must be inhibited.

The Segmenter has been designed to work
wi th both the Program Test System and the

Executive System monitors.
The Program Test System, Honeywell's
checkout system, allows dynamic or snapshot
dum?ing of memory areas and tapes during the
program operation. The dumping occurs at
points where the programmer requests derail
linkages to the monitor. The requested
dumping is identified by the location of the
derail. The mobiLity of the segments created

FACT SEGMENTATION

311

a problem that was handled by including the
segment number in the derailing instruction.
Use of the Segment Control Table allol..red a
routine to convert the derail location to a
location relative to location zero. The
particular derail could then be identified.
The instructions dumped are converted via use
of the Segment Control Table to locations
relative to zero. Thus, the programmer need
not be hindered by the actual position of the
segment while it was being dumped.

The Executive System .~ll be the pri~~
monitor working with the Segmenter. Each FACT
program is given an area of memory to operate
in at scheduling time. The full power of the
Executive System Monitor is available to the
FACT programs. It is used to set restart points,
restart individual programs, execute a full
schedule of parallel operating routines, test
the validity of the schedule, etc. Loading
of segments is done by the Run Supervisor after
receiving the information from the Segmenter.
The search for a new segment on the Production
Run Tape is always optimized to the proper
direction.
Operating

Exp~rience

That described in this paper is not a
proposed or theoretical system but one that
has been in daily operation since August 1961.
There have been e.mbellishments to improve the
Segmanter, but it has not changed in its
basic operation.
In September 1961, the Segmenter was tied
into the Executive System. Runs have been
scheduled and executed involving combinations
of two FACT programs and an assembly language
program all operating in parallel. In that
operation there are periods where five of the
eight independent sequence counters in the
H-800 are active. All eight of the sequence
counters were used at some time during this
operation.

Future Modifications
A number of ideas have been su?gested to
add to the flexibility and attractiveness of
the Se~nenter. Currently the Segmenter requires
about 500 memory cells. There is a separate
segmenter for each FACT program being run in
____ 1.,_1

iJCI•.J:"C:iJ..J..t:::.L..

'- __

1- _ _ _

vt:::~U.llJ..yut:::

Ud,::i

ut:::t:::u

..L _ _

1-_.!_~

..l ____ , _ _ _ - l . L . _

ut::: vt:::.L.u!Jt:::u

have only one Segmenter for all FACT programs
in operation. The FACT programs could h:1Ve
their segments intermingled in memory instead
of having distinct areas as is now required.
The most difficult part of this design would
be the setting of restart points. The Segment
Control Table would be employed to identify
the areas occupied by the segments of the
program for which a restart was being set.

To further conserve memory, the operations
of the Segmenter would themselves be segmented.
The Segment Control Table is the source
of information to the Segmenter as to the size
of each segment. This table could have its
entries changed by the program and enable
specified segments to grow in size according
to the dynamic needs of the routine.
The Segmenter makes no attempt to save
the settings of a segment it is about to
destroy. Such a segment could be dwupad L,to
secondary storage prior to its destruction.
A choice could be made when the segment was
again called as to having it loaded in its
initial state or in the state it was in the
last time it appeared in memory.
AcknOWledgements
Acknowledgement should be given to the
staffs of Computer Science Corporation,
Inglewood, California, Philip Hankins and
Company, Inc., Arlington, Massachusetts and
the Honeywell FACT Group for their work in
the design and implementation of that
described in this paper.

l'ROGRA~I~IIi\'G

312

AND CODING

SEGMENT CONTROL TABLE
SEG. NO.

STATUS*

LENGTH

FOLLOWER~~

LOCATION

BANK 0

BANK 1
i

0.,
"'"
2
3

500
500
400
200
600
600
300
900
200
300
300

A
T

"'"

0
A

5
6

A
I

8
9
10

0
0

0,0$00
0,1000

1,0000

8
L

1,0200
0,1.500

1,0800

1
4.

EXECUTIVE
MONITOR

SEGM"r:NTER
SEG. 0

BANK CONTROL TABLE
BA.~K

NO.

FIRST
SEG.

LAST
SEG.

UNUSED
STORA.GE

LOv-lEST
LOC.

HIGHEST
LOC

1000
1000

500
000

1999
1799

0
3

0
1

LOWEST
LOC UNLOADED

1800
1000

Fig. 1 STARTING CONDITION OF EXAMPLE

SEGMENT CONTROL TABLE (PARTIAL)
SEG. NO.

STATUS

LENGTH

FOLLOWER

LOCATION

A
A

500
500
400

1
6

0,0500
0,1000

1
2

I--_=;;.;....-~_,OOO

etc.
BANK CONTROL TABLE
BANK
NO.

FIRST
SEG.

LAST
SEG.

UNUSED
STORAGE

LOWEST
LOC.

HIGHEST
LOC.

500
1000

500
000

1999
1799

8
Fi~.

*
-Be

LOWEST
LOC UNLOADED

1800
1000

2 ACTIVATE INACTIVE SEGMENT 1

A = ACTIVE; I = INACTIVE, in HSM; 0
L = LAST SEGMENT IN BANK

= OUT

OF HSM

SEG. 3

SEG. 5

313

FACT SEGMENTATION

SEGMENT CONTROL TABLE
SEG. NO.

BANK 1

STATUS

LENGTH

I
A
A

200
300
300

LOWEST

8
9
10

FOLLOWER

LOCATION

1,0800
1,1000
1,1300

SEG.

BANK CONTROL TABLE
BANK

FIRST

LAST

UNUSED

NO.

SEQ.

STORAGE LOC.

0
3

6
10

500

400

500
000

HIGHEST
LOC.

1999
1799

LOWEST
LOC. Tn.TT f"'. AT'lt;'T'I
Vll~l1J.J.L:.I..u

1800
1600

Fig. 3 LOAD SEGMENTS 9 and 10 INTO END OF STORAGE

SEGMENT CONTROL TABLE
SEG. NO.
--

STATUS

I
A

LENGTH

FOLLOWER

600
600
300

8
L

LOCATION

1,0200
0,1500

BANK CONTROL TABLE
BANK
NO.

FIRST
SEG.

LAST
SEG.

0
1

6
10

UNUSED
STORAGE

500
1000

Fig. 4 RELEASE SEGMENT 5

LOWEST
LOC.

0500
0000

HIGHEST

LOC.

1999
1799

LOWEST
LOC. UNLOADED

1800
1600

314

PROGRAMMING AND CODING

BANK 1 (before)

SEGMENT CONTROL T.<\BLE
SEG. NO.

o
1

LENGTH

FOLlOWER

LOCATION

1
6

0,0500
0,1600

1,0000

500
500
400
200
600
600
300
900
200

0,1500
1,0800

300

200

1,0200
1,0500

STATUS

--A-

6
7

I
A

9
10

BANK CONTROL TABLE
BANK FIRST LAST UNUSED
NO.
SEG.
SEG. STORAGE

--0 0 - --0
1
3
7

500
100

LOWEST
LOC.

HIGHEST
LOC.

000

SEG. 3

BANK 1 (after)

SEG.

SEG. 9
500

SEG. 10

SEG. 7

~~~~~~OOO

SEG. 9
LO\\~T

LOC. UNLOADED

1999

1800

1799

1700

~15

FIG. 5 LOAD SEGMENT 7 INTO AN OPENING

SEGMENT CONTROL TABLE
FOLLO~lliR

BANK CONTROL TABLE
BANK FIRST LAST UNUSED
NO.
SEG.
SEG. STORAGE

-0- - 0 - - 9 1
10
5

LOCATION

0,0500
0,1000

0,1500

1,1100

1,0200

L
7.

0,1700
1,0000

LOWEST
LOC.

000

soo--

HIGHEST
LOC.

000

1999
1799

FIG. 6 LOAD SEGMENT 5 AFTER SQUISHING

NK 1

]

J
EXECUTIVE

SEG. 10

500 ~
I---------l

SEGMENTER
SEG. 0

SEG. 7

t-------=rOOO ~
LOWEST
LOC. UNLOADED

2000
1800

SEG. 1

b=100~
I j ,- '- __
SEG.

SID. 9

-oJ

315

FACT SEGMENTATION

SEGMENT J
REFERENCE REGION
TAG

REFERENCED
SEGMENT
ar- SEG. 1
R2
SEG. 5
R3
SEG. 9
STARTING CONDITION

REGION CONTROL WORD
LOCATION
0,0210
1,0500
0,0181

BAD
PARITY
x

Rl
SEG. 1
0,1210
R2
SEG. 5
1,0500
R3
SEG. 9
0,0181
SEGMENT 1 ACTIVATED
Rl
SEG. 1
R2
SEG 5
R3
SEG. 9
SEGMENTS 9 and 10

COMPLETE ADDRESS CONSTANTS
INSTRUCTIONS

R1
R2
R3
LOAD

SEG. 1
0,1210
SEG. 5
0,0)00
x
SEG. 9
1,0381
SEGMENT 7 (MOVE SEGMENT 9)

Rl
R2
R3
10 AD

SEG. 1
0,1210
SEG. 5
1,1500
SEG. 9
0,1881
SEGMENT 5 (MOVE SEGMENT 9)

FIG. 7 CHANGES TO SEGMENT 3
REFERENCE REGION WORDS

MASKBASE CONSTANTS
SPECIAL ADDRESS CONSTANTS

0,1210
1,0500
1,1181
LOADED

0,1210
Rl
SEG. 1
R2
SEG. 5
0,0300
1,1181
R3
SEG. 9
RELEASE SEGMENT 5

REFERENCE REGION

UNRELOCATABLE CONSTANTS
AND DATA STORAGE

FIG. 8 TYPICAL FACT SEGMENT STRUCTURE

317

A GENERAL TEST DATA GENERATOR FOR COBOL
Lt. Richard L. Sauder
Automation Techniques Branch
Headquarters, Air Force Logistics Command
Wright-Patterson Air Force Base, Ohio

'l'lll.S ar"t.l.Cl.e Q.l.scusses the effort being made
by the Air Force Logistics COImlland in developing
a method of generating effective program test
data. This "Test Data Generator" is designed to
operate in conjilllction with the ~ compiler
implemented by AFI..J:;. As such, the system not
only builds data conforming to descriptions given
in the Data Division of a COBOL program but also
places in these items necessary data relationships to test the logic of the COBOL program.
Both the utilization and the method of operation
of the system are discussed in this paper.
Introduction
One of the major underdeveloped areas that
still exists in the development of programming
techniques is that of insuring adequate checkout
of programs before release for use. Often the
logical paths wi thin a program are highly complex. The effort to insure that each of these
is functionally correct can be prohibitive - so
much so that only the most obvious and most frequently employed segments of the program are
tested thoroughly.
Compilers that have been employed in the
past decade have aided in reducing this problem.
By eliminating many careless coding errors, they
have not only insured a greater degree of operation in a shorter time but have also released
more time for more elaborate testing of the compiled program. The fact still remains, however,
that unless adequate test data is available the
debugging effort is hampered. Recognizing this
deficiency, the Air Force Logistics Command last
year began developing a method of producing this
data. The immediate result is a Test Data Generator designed to operate in conjunction with the
COBOL compiler implemented by AFLC. As such it
performs two main filllctions:
1. Builds data of the format and description specified in the COBOL source program and
2. Inserts in these elements data specified
by the user to meet inter (and intra) element
requirements and relationships.

nent criterion is that of controlling the content
of these elements.
The method of operation and the information
necessary to fulfill these functions will now be
described in detail.
utilization of the COBOL Data DiviSion
Determining the format of data fields results from a thorough interpretation of the Data
Di vision of the COBOL source program being
tested. Wi thin this Division, options exist to
describe in detail both the structure of every
element wi thin a record and the relationships of
these elements to one another. Those options
which affect the generation of data are defined
as follows:
1. ~
2. Level number to establish the relationship of one unit of data to others.
3. Size in number of characters.
4. Class indicating the type of data, i.e."
alphabetic, numeric, alphanumeric.
5. Usage to establish the number system in
which the element is represented.
6. ~ to define repeated occurrences of
the same element.
7. Range to establish limits for the value
of the element.
8. .§!B!l specifying the operational sign of
the element.
9. SYnchronize poSitioning the element
within or across computer words.
10. Redefines to allow the same area to have
more than one description.
11. Picture - a graphical representation of
the element.
12. ~ to define a stated value for the
element.

In addition to these element descriptions,
options are present which describe the files to
which the records belong, e.g., tape and file
labels" the number of records within a file and
the number of elements within these records.
Construction of Formatted Data

These functions basically fulfill the needs
for prodUCing effective test data. Obviously it
is necessary to produce elements conforming to
their given fonnats. But Since there are few
business oriented runs which do not require dependency among various elements, a more perti-

Since in the generation of data we are concerned only with those records in a program deSignated for input, the interpretation of the
source program Data Division produces only sets
of parameters dealing with elements of input
records.

PROGRAMMING AND CODING

318

In all cases this' set includes the size of
the element of data and its relative location
within the record. Other information produced
depends on the type of element. Type in this context is deflned as one of four classifications:

1. Li teral indicating that a single value
has been defined for the element.
2. Conditional indicating that a restricted
set of variables only may appear in the field.
(Conditional values in COBOL data descriptions
are designated by a level number of 88.)
3. Random indicating that no values were asSigned to the field so that the content of the
element is determined only by the options: class,
range, and base.
4. Sequential indicatL'"lg tha.t the original
value of the element is to be incremented by a
fixed or a random amount.
Jl.ll information concerning these types can
be obtained from the data descriptions with the
exception of those items to be sequenced, and the
amount, if known, by which they are to be incremented. Therefore, disregarding these items, it
is now possible to generate "garbage" test records with only the COBOL source tape for the
program serving as input. The method of generation if this were desired 'WOuld be as follows:

1. Interpretation of the program's Data Division, construction of sets of parameters and
grouping of these parameters by record designation.
2. Isolation of all parameters for a partiCular record and employment of each set of parameters, in turn, to build a Single test record with
the following criteria:
a. If the element is li teral or conditional, insert the value or chosen value into its
relative position in the record.
b. If the item is random, generate random characters (determined by the class of the
item) filling the element.
3. Repeti tion of step t'WO until the desired
number of test records has been generated.. Repetition of the entire process for the next record
description, and so forth.
In testing applications, it is often true
that some information which 'WOuld be generated in
this manner is insignificant or unnecessary. For
instance, a thirty character random field reserved
for a manufacturer's name could possibly be deleted or replaced by a two character code representing the name if this element is not involved
in any logical decision in the program. This action 'WOuld not only reduce the time needed for
generation, but also 'WOuld considerably improve
the appearance of the data. In addition, elements
may not be described in the Data DiviSion to a
sufficient degree for testing purposes. For instance, a stock-number may be described as alphanumeric when in reality the first half of the
number is alphabetic and the remainder numeric.

For these reasons the Data Generator includes
the option to modify data descriptions by the deletion or replacement of these descriptions or by
the insertion of new descriptions. The method by
which these modifications are expressed will be
discussed later.
Specification of Data Relationships
The data generated in the manner described
falls far short of being adequate for production
testing. Though some control on the ccntent of
the records is obtained by stating literal and
conditional values for elements, the great majority of the output is unrelated "garbage" adequate
only for testing error logic. For this reason
the ability to specify data relationships and requirements is included with the generator. The
type of relationships desired may be of the following nature:
If fie1d-1 of record-A equals field-1 of record-B then field-2 of record-A must be in
the range 7-15. If fie1d-2 of record-A is
less than 10 and field-3 of record-A is not
less than 24 then field-7 of record-B must
equal "A"; but if field-2 of record-A equals
10, then field-7 of record-B equals "C". If
fie1d-7 of record-B equals "C" then fie1d-8
of record-B equals 0 or 2 • • • • •
Via this option the formatted records produced can be edited to contain combinations of
these relationships, which in turn can test the
logiC of the program concerned. To allow a flexibility of this magnitude, a procedural type
system similar in objective to the COBOL Procedure
Division is provided. Just as the Procedure Division contains a series of statements arranged to
specify the logic of a computer program, thi s
system (named the Relation Section) is a series of
statements arranged to specify the logic of data
relationships.
The Relation Section is formed by a series of
conditional and declarative statements consisting
of a restricted set of operations and the operands
involved. The operands are those element names
which appear in the Data Division of the program
or those defined by the method of modification
explained before, and any quantity appearing as a
1i teral value. The same conventions apply to expressing these operands as in the COBOL Procedure
Division.
Example:
If FIELD-l equals SUBFIELD-X of FIELD-A of
REroRD-1 •
If CLASS-CODE-l equals "ABC" then IN-CODE of
FIEID-C equals 375 • • •
~ne set of operations allowed consists of
three types: relational" arithmetic and control.

319

A GENERAL TEST DATA GENERATOR FOR COBOL

Relational Operations

Control Operations

The relational elements are the same as those
defined in the COBOL language for expressing conditional relationships. In the Relation Section,
however, these elements serve a dual purpose.
.They first express conditional relationships as in
COBOL. In addition, however, they are employed in
imperative statements to prescribe an action between given operands. Used this way, the convention is established that given

At present three control operations are permitted.
1. l!m. denotes completion of data specifications •
2. 9Q to path-i.
Example: If FLD-R EQ 7 and FID-P NLS 100, GO
'ro AB-l; otherwise GO ro AB-2.
AS-I. ENG FID-H is • • • • • •

oprnd-m (relation) oprnd-n,

BUIID record-name-j.
This operation signals the construction of a particular record
described in the Data Division.
If references are made to elements
wi thin a record for which the BID
option has not been stated, these
items are ignored.

oprnd-m is adjusted, if necessary, to satisfy the
given relation. For instance, given: FID-A equals
FLD-B. If inequality exists, the content of
FID-A is made equal to that of FIn-B.
The relations (and their associated mnemonics) are:

F.Q
NF.Q
GR
NGR
LS
NLS

The option simultaneously releases
a record which has been constructed and initiates the construction
of a new one.

equals
is not equal to
is greater than
is not greater than
is less than
is not less than

EKample:

ZER

is~

NZR

is not zero
is positive
is not positive
is negative
is not negative
range of (elernent- j) is
(value-a) - (value-b).
(value-c), (value-d), ••• (value-m).

FOS
NBS

1.
2.

BID REl:X)RD-l, REI::ORO-2.
If ITEM-CODE is POS, BID
REmRO-3.

Additional Relation Section Options

If FID-B

FID-3B of REI:D-l NNG; FlD-2A of FID-2 of
REm -B lim. FID-2B.

Several storage areas of varying sizes are
set aside for use with the Relation Section.
.Each of these areas has a fixed name and may be
referenced as an operand by any appropriate operation stated. The major reason for providing
these areas is to allow trailer type items to be
specified. For instance, if a stock-number of an
item must appear in fifteen successive trailers,
this stock-number can be generated and placed in
a storage area and then be moved later to the appropriate element when the trailer items are
built.

If ELEMENT-C GR 7 or if ELEMENT-P EQ
"AB", RNG FID-3A is 7-19.

These areas must be used when an element of
a table is referenced by subscripting.

NEG

NNG
RNG

Examples:

.m. FID-C,

ITEM-NO-l

200017.

4. !mQ. ITEM-PQ is "A", "B", "D", "X", 9, 13.
Arithmetic Operations

*
/

element-j
element-l
element-n
element-q

PillS element-k
MINUS element-m
TIME§ elernent-p
DryIDED BY element-r

Examples:
1.

If FID-E EQ FID-C

ELEMENT-I
2.

* 3.

+ FID-D,

If TRALR-CODE-l EQ I, BIID-19 EQ
STOCK-NO-l. • • • •
• • • • BID TRLR-REDJRD-IA. SroCK-NO
OF TRLR-RECORO-IA EQ BILD-19 • • ~
BIlD-6 EQ 7. If TA:8LE-l (BIID-6)
EQ • • • •
NOTE: BILD-6 and BIlD-19 are names of assigned storage areas.

then ITEM-l EQ

If ELEMENT-B - 35 GR 7, RNG FID-F is

0, 1.

Examples.

Preparation of Relation Section for Input
The examples that have been given for the
use of the Relation Section have indicated a

320

PROGRAMMING AND CODING

moderately free format. On the contrary, a tabular form of input has been chosen because the task
of specifying the operands and the desired operation (or operations) is generally simplified by
employing tables. Two tables - one containing operands, the o~ner containing operations - are required to specify a set of relations and actions.
Figure ~ describes the formats of these tables.
In this illustration also is the tabular representation of the following series of statements.
Al.

If IN-l

m FID-2,

then SroCK of RECORDof REroPJ)-2, BIID-6
5,
TBL-l (BILD-6) GR TBL-2 (BILD-6).
If START-CODE NLS 4, then RNG FID-18 is
"A", "B", "X", go to A5; otherwise go to
A4.
BID REmRD-C. Go to A5.
BID REroRD-A, REU)PJ)-B. Go to A3.
A

A2.
A4.

A5.

m S'IDCK

In this tabular form, series of disjunctive

statements are expressed horizontally across successive columns; conjunctive statements are expressed vertically in .2llE. column. For example,
given the series of expressions:
If (A m B and C LS D) or J NLS K or
(E NQ "X" and F FOS), THEN BID Q.

Only those input files for which test records are
to be constructed must be listed.
The SE;iUENCE option is specified in the following manner:
SmU.l!l'l"CE (Name) (Orig. value) (Increment).
Examples:
CONTROL SEl:TION.
COUNT
FILE-l
RECD-A
RECD-B
COUNT
FILE-2
REl:I)-C
SEQUENCE
FlD-ZC
OF RECD-B
.E!LFlvl-Pl
SmUENCE

5000
1500
7000
100000

100

ABCDE

Overlay Section. This section contains those
elements of the Data Di.vision which are to be modified. imY of three options may be employed depending upon whether an element is to be deleted,
replaced, or inserted. (The "line-number" referred to in the following explanations is that
found in the COBOL Data Division.)
1.

This series is expressed tabularly as fol-

Deletion:
line-no-l DEI' ET'E

(thru line-no-2).

lows:
NAl, and I will be employed,
cedure-oriented languages~ the description techand the classes < INTEGER> and
nique which is most natural is the preferred one,
are assumed to be already defined. Let the
and the contention here is that the structures and
class of formal representations of these descripdescription technique to be defined are the natural
tions be called FIELD, where this is defined by
ones for many data sets.
::= «INTEGER» I
An English language description of the set of
«INTEGER>, );
structures under consideration might help in under- ::= I .
tures under consideration are, broadly, those
Using single Roman capitals as IDENTIF,:-IERs, the
that can be presented in an "outline" or "list" or
following examples of FIELDs can be given:
"level" form, with the additional property that
A (4)
multiple instances of any "level" can occur. For
A (4, B(5»
example, a personnel file might be made up of 40
A (4, B(5) C(6»
records, each record being composed of; say;
A (4, B(5, D(3) E(2» C(6».
three distinct items - - name, salary history, and
work evaluation list. The item "salary history"
The personnel file above would have the form:
may allow for the ten most recent raises and
P (40, U(20) S(10, D(6) T(5» E(10, R(2»).
dates; the item "work evaluation list" may proThose
structures definable by FIELDs will be
vide for the ten most recent ratings. In outline or
referred to as generalized structures, and an
list form, the items might be stated as
interpreted FIELD will be referred to as a gen-

327

DATA STRUCTURES THAT GENERALIZE RECTANGULAR ARRAYS

eralized structure descriptor, or, simply, a descriptor.
If FIELDs defined as follows:
::= «INTEGER»
«INTEGER>, 1 such that
C i = Ai and Yi = Xi' for i < t, and
C t precedes At in the FIELD SEQUENCE
that defines A t - 1 , or

There exists at> 1 such that
Xi, for i < t, and

The position in the linear array. then. of a particle. PlJ referenced by {(Ai. Xi)}, i = 1, ...• k,
is equal to the total number of particles that precede P l , by virtue of 1, 2, or 3, above. It is
clear that these conditioris are mutually exclusive;
that is, particle P 2 can precede PI by virtue of
only one of these conditions, and if the conditions
2 or 3 are pertinent, then a specific t is involved.
Thus, 81 is defined to be the total number of particles that satisfy condition 1, rr t to be the total
number of particles that satisfy condition 2 for t,
and !:1 t to be the total number of particles that satisfy condition 3 for t, where 2 s t s k. It follows
from the above that the sets comprising these totals are diSjoint sets and the number of particles
in their union is the total number of particles preceding Pl' Thus, the position of P l is given by
k

(OJ; + St)·

t= 1

where al = O. What this means in terms of the
L-tree is demonstrated next.

DATA STRUCTURES THAT GENERALIZE RECTANGULAR ARRAYS

For each leg node (or FIELD), F, let M(F) be
the total number of particles that lie below each
of the n legs of F. If the legs of F are particles,
M(F) = 1. Let N(F) = n· M(F). Note that, if
B l , B 2 , '" , B· are the FIELDs in the FIELD
SEQUENCE for ~ (that is, successive branches
of a branch node), then M(F) = r~= 1 N(Bi)' Let
i-1
us define Q(B l ) = 0, and Q(Bi) = L {= 1N(B t ) for
i = 2, ... , j. Note that Q(Bi) is the total number of particles below B l , B 2 , ••• , B; -1 .
It should be clear that, , for P l given- by [(Ai,
xi) }, i = 1, 2, ... , k,
81 = M(Al)(x l -1), 8 t = M(At)(xt-1), and at = Q(A t ).
Thus, if for each FIELD (or IDENTIFIER), F,
the quantities Q(F) and M(F) are computed, the
particle referenced by [(Ai> Xi)} is to be found (or
placed) in the position of the linear storage numbered:
k

I [Q(Ai) + M(Ai)(Xi- 1 )].
i= 1

where Q(A l ) is set equal to O.
The Q's and M's can be computed at compile
time quite readily, given the generalized structure descriptor. The amount of storage reserved
for such a structure is N(A l ) = alM(A l ) particle
positions. At run time, when the xi's and Ai's are
supplied, the relative address is easily computed.
Note that the Ai's must be supplied in this general
case, in addition to the xi's -- for n-dimensional
arrays only the xi's need be given -- since not all
particles are derived from the same set of A's, although all of the particles have Al in common.
It is interesting to note the relationship of these
quantities to the quantities in the storage mapping
function of an n-dimensional rectangular array.
Let the generalized structure descriptor be Al (a l ,
A:;>(a:;?, ... , Ak(ak» ... ). Since each FIELD
SEQUENCE has only one FIELD, Q(Ai) = 0 for
each i. Now, M(A k) = 1, N(Ak) = ak' 1 = ak,
and M(Ak-l) = N(Ak) = ak' In general, M(A j _1)
N(A j ) = aj" M(A j ). Thus, by induction,

329

upon receiving the generalized structure descriptor at compile time, then the computations that
would be carried out at run time when presented
with reference expressions.
The first task ot the program is to place the input FIELD into a vector, one word for each symbol.
A table is then constructed which has one row for
each identifier or FIELD of the input. This table
is, in some respects, similar to a Perlis 3 threaded list; the same names for the columns have, in
fact, been adopted.
The f column of the table is defined, for the
FIELD (or IDENTIFIER or ROW) named A, as follows. If A is a FIELD of the form A(n), then f(A)
is 2 or 0, depending upon whether or not A is the
last FIELD in a FIELD SEQUENCE. If A is a
FIELD of the form A(n, Bl ( ) ... ), then f(A) is
3 ::>r 1, depending, again, upon whether or not A
is the last FIELD in a FIELD SEQUENCE.
The t column is defined as follows. It A is of
the form A(n, Bl ( ) B 2 ( ) . . . ), then {,(A) is B 1 ;
if A is of the form A(n), teA) is undefined.
For the r column, if A is the overall FIELD, r
is undefined. If f(A) is 0 or 1, then rCA) is the
succeeding FIELD in the FIELD SEQUENCE in
which A occurs. Otherwise (that is, f(A) is 2 or
3), r is the FIELD which is defined by the FIELD
SEQUENCE of which A is the last FIELD in the
sequence.
Finally, a c column is defined; this column has
no counterpart in threaded lists. For each FIELD.
A, the c column contains the associated INTEGER
in that descriptor; that is, whether A is of the form
A(n) or A(n, Bl ( ) ... ), c for that A is n. No
information appears in this table that is not in the
original descriptor, although the table is now in
a more usable form for computing the N's, M's
and Q's.
If f(A) is 0 or 2, M(A) is set equal to 1, and
N(A) is set equal to c(A). From this point on, the
task is reduced to finding a FIELD (defined by a
FIELD SEQUENCE) all of whose FIELD SEQUENCE
components have their N's already defined. Thus,
if A is defined by A(n, Bl ( ) ... Bk(
then

»,

M(A .) =. 1} ai, for j = 1, ... , k - 1.
J
l=J+ 1
This is precisely the expression for the p' s derived above for rectangular arrays.
This completes the assertion that the description method, reference expressions, and storage
mapping functions for generalized structures are
direct generalizations of those for n-dimensional
rectangular arrays.

M(A) =

N(B i ),

i= 1

and N(A) = c(A)· M(A), where, of course, c(A) = n,
in this case. At this time Q(Bi) can also be computed for these i's by

j-1
Storage Manping Function ComputatiQD

)J N(Bi)

= Q(Bj-1)

+ N(B j _ 1 )·

i= 1

Appendix A is a Burroughs ALGOL program::!
for the Burroughs 220 computer which simulates,
first, the computations carried out by a computer

This process is iterated until N(A) is found for the
A which is the overall FIELD being processed.

330

PROGRAMMING AND CODING

This processing is carried out by constructing
Q(U)
0
an incidence matrix, G, by using the f, t, and r
Q(S)
N(U) = 20
columns, such that the matrix has as many rows
Q(E) = Q(S) + N(S)
130
and columns as there are FIELDs, and has a 1 in
Q(P)
O.
row A, column B, if B is in the FIELD SEQUENCE
defining A. The A's for which M's are ready to
Thus, in tabular form:
be computed are then determined by comparing the
Q
M
N
rows of G to a vector which has l's for those FIELDS
P
150
6000
0
for which N is already determined.
The G matrix is constructed by finding, for each
1
20
a
U
FIELD. A. for which f(A) is 1 or 3, the con.stituents of its FIELD SEQUENCE, by looking at ,(A),
11
110 20
S
r(-f(A), r(r(, (A»). etc., until r( ... r(J.(A» ... )
= A. All of the FIELDs so encountered are con1
D
0
6
stituents. The ord'3r in which the FIELDs are
encountered is later used (when the N's for the
1
5
T
6
FIELDs are known) in computing the Q's of 'these
constitutents of the FIELD SEQUENCE, A.
20 130
2
E
These computations are now summarized for
the example above. The input, as before, is
1
0
R
2
P(40, U(20) S(10, D(6) T(5» E(10, R(2»).
The 6000 ln this table indicates the total storage
required for this FIELD; beyond this point, only
the M and Q columns need be retamed for proThe following table is constructed (where means
cessing the reference expressions at run time.
undefined ):
Next to be considered is the manner in which
c
f
r
t
this data would be used to determine the position
indicated by the reference expression f (P, 2), (S,
P
1
40
U
3), (T, 4)1. Using the storage mapping function,

*
*

f (X)

= 0:

[c(X)

f (X)

= 1:

=
=

t. ,(XI

to reX! (except If X is overall FIELD!
from last FIELD in FIELD
defining X

SEQUENCE

lO.l(X)

•

to r(X)

1
20
1
6
5
1
2
0
N{D) + N(T) = 11
10· 11 = 110
0
6
N(R)
2
10·2
20
N(U) + N(S) + N(E)
40· 150 = 6UOO

C(x)F
I

The following are then computed in order:
M(U)
N(U)
M(D)
N(D)
M(T)
N(T)
M(R)
N(R)
Q(R)
M(S}
N(S)
Q(D)
Q(T)
M(E)
N(E)
M(P)
N(P)

f--

'(X1~

I
I

83
to r (X)

f (X!

03--

from

last FIELD in FIELD SEQUENCE

defining

loRex)

150

Fig. 4.

Definition of "Boxes" in Terms of the
Quantities f(x), t(x). r(x), and c(x)

DATA STRUCTURES THAT GENERALIZE RECTANGULAR ARRAYS

L:[ Q(A i ) + (xi - l)M(A i )J = [0 + (2 - 1)· 150J +

[20+ (3 -1)' 11J + [6+ (4-1)· 1J

15 0 + 42 + 9

----- -

Fig. 5.

= 201

------------_-,
I
I

"Box" Diagram for P(40, U(20) S(10,
D(6) T(5» E(lO, R(2» )

331

and six-bit characters in others, for example, then
clearly the d'2scriptor, reference expressions, and
mapping function must reflect this. The problems
here seem reasonable to handle, but, of course,
the descriptor definition must be modified.
In keeping with the notion, alluded to before,
that structure definition is distinct from instances
of that structure, the IDENTIFIERs could be removed from a descriptor, and the remains considered as a structure definition. In terms of the
L-tree, the effect would be merely to remove the
IDENTIFIERs -- the tree does not change. In declaring data which has such a structure, it would
be necessary only to supply a sequence of IDENTIFIERs which could be interleaved with the skeletal
representation, placing one before each left parenthesis. Using the example once again, the structure could be defined as
(40, (20) (10, (6) (5» (10, (2»).

There is another useful pictorial method for
representing the structures under consideration.
This method is easily derived directly from the
descriptor. Each FIELD has a "box." Two sections are associated with each box. The first
sec tion contains the IDENTIFIER. X, of the FIE LD;
the second section contains c(X). There are arrows emanating from and entering the boxes, the
nature of which depends upon f(X). This dependence is given in Fig. 4. Using these definitions,
the descriptor
P(40, U(20) S(10, D(6) T(5» E(10, R(2»)
can be indicated as in Fig. 5.
Further Considerations
There are several questions concerning generalized structures which are still under consideration, bu.t for which results cannot be presented at
this time.
The first of these questions involves a more general definition of FIELD which allows a (previously defined) FIELD to be referred to by FIELD name,
alune, withuut indicating the associated FIELD SEQUENCE, or the number of data particles. In addition, the generalization from INTEGER to ARITHMETIC EXPRESSION is highly desirable, but
will, of course, delay the M and Q computations
until run time. Tne same delay is incurred in computing the coefficients for the storage mapping function for n-dimensional rectangular arrays, when
arithmetic expressions are used in the descriptor.
A second area of present and future interest is
that of nonhomogeneous memory and/ or data. For
example, the particles of data may not be the same
throughout. If single bits are used in some places,

The instance noted above could now be declared
by naming this skeletal structure and providing the
sequence of IDENTIFIERs P, U, S, D, T, E, R.
The M's and Q's can be determined from the skeletal structure alone, and are usable for any subsequent instance. All of this is, of course, a notational simplification for writing the structure descriptor in terms of free-variable IDENTIFIERs,
and then binding these IDENTIFIERs by a sequence
of IDENTIFIERs.
It is interesting to consider the set of such skeletal structures as being in reality a generalization
of all Euclidean spaces; that is,
::= « INTEGER;') I
«INTEGER>, ::= I

defines a set of formal objects, < GENERALIZED
POINT>, which is a direct generalization of the
collection of all n-tuples of integers for all n.
Acknowledgment
The author wishes to thank Mr. K. Speierman,
who suggested t.~e value of a study in this area, and
who made many useful contributions to the completion of the wor k.
References
1. J. W. Backus, "The Syntax and Semantics
of the Proposed International Algebraic Language
of the Zurich ACM-GAMM Conference, II presented at the First International Conference on Information Processing (ICIP), June 13-23, 1959, i~
Paris, France (IBM Corporation, New York).

PROGRAMMING AND CODING

332

2. (Burroughs Corporation), "Burroughs Algebraic Compiler - A Reference Manual, " Bulletin 220-210 ll-P, January 1961.

BEGIN

EITHER

3. Alan J. Perlis and Charles Tnornton, "Symbol Manipulation by Threaded Lists, ,; Communications of the ACM, April 1960, Vol. 3, No.4, pp.
195-204.
Appendix A - Burroughs ALGOL Program
OR

The following is taken directly from the printer output of the Burroughs 220 computer, as employed for the Burroughs ALGOL program as deSf'1"ihorl

above.

INTEGER

WHEN THIS IS COMPLETED.
REFERENCE EXPRESS I ONS$
OTHERIIII SES

THE PROGRAM

IS "EAD'"

KAPPA ••

TO A<'CEPT

ARRAY
INIIOO) .BI2'5) .P(25) .C(25) .L(25) .S(25) .K(~C;) .KP(25) .1'<1(25).
F (25).R (25) .RN(2'5) .LN(2C;) ,SIG 12c;) .TAUI?5) .N(25) .GI?5.25).
T ( 2'5 ) • TN I 25 ) • a ( 25 ) $
INPUT
FIELD(KM.FOR I =(l.I.KM)$IN(J)l$

FORMAT

HEAD (BCh"J* ,SIS. *8 (J )*. 86_ *'F (J '*.86' *L (J l* • Flf" *R (H)* ,86,
*C (J )*.S6.*N(J») *.S6.*M( J)* ,S6.*c;. (,J)*'. \1,'2)$

I'"ORMAT
FORM I II 0.B9.AI • II 0.B9. AI .B9. AI. 110. 110. 110. 110. WO) $
OUTPUT
TABLE(FOR J= I 1.1. JM)$ (J.B (J) .F( J).L (J) .R(J).c (J).N (:J).
"IJ)'O(J)l)$
TAKE IN..
READ(SSFIELD)$
COMMENT
THIS ASSIGNS SUCCESSIVE VALUES OF J TO INPUT
FIELD IDENTIFIERS. IDENTII'"IERS ARE STORED IN BIJ).
THE POS I T I ON I N THE I "lOUT S T"II "IG OF B ( J) I SIN P (J ) •
JM is THE LI'IIT OF J$
COMMENT
NOTE THAT LEFT PARENTHFNSES ARE STORED AS
')400000000. RIGHTS AS 24000(30)0. AND CO .... /IS AS
2300000000.
INTEGERS f) TO 9 ARE STORED AS BOOOOOOOOO.
8100000000. ETC.$
J=IS
FOR KA= ( ! 01 .KM) S
BEGIN
IF (IN (KA) NEO 0400000000) AND (IN (KA I NEO 2400000000 I
AND C/N(KA) NEO 2300000000) AND I ( C~SE FI.;)=O.
OR 2. TH[S SETS N(J)=CIJI. MIJ)=I. AND KIJ)=l.
IN
GENERAL K I J I III I LL EQUAL I ONCE "I I J I HAS B~EN
DE TERM I NED$
FI 11=1$
I'l!! )=0$
RNOI=O$
FOR KA: (! oI.J"')$
IF B(KAI EOL L(I)$
LN (I )=KAS
FOR J=1201.JM)$
["I (KB)

NEO 2300000(00)$

END$
!INISJ) FOL 2400000000)
BEG[N
KOIJI=I !L

liND

IINIPJ)

NI'"O ?3001"'t00r)OOI$

KA=I$
IF S(KA) NEO SJ$
BEGIN
KA=KA+ 1$
GO TO KAPPA$
101'.10$
R(JI=BIKA 1$
RNIJ)=KA$
END$
OTHERWISE$
BEGIN
F IJ )=3$
KA=I$
IF S (KA) NEO SJ$
BEGIN
KA=KA+I'$
GO TO LAMBDA$
10"10$
R (J I=B(KA 1$
RNIJ)=KA$
FOR KA=lIo1.JM)$
BEGIN
IF BIKAI EOL LIJI$
LNIJ)=KA$
END$
END$

END$
COMMENT
THIS FILLS THE ROWS OF G FOR F(JI=I OR 3$
FOR J=(loI.JMI$
BEGIN
IF (FIJ) EOL I ) OR IFIJI EOL 31$
BEG[N
X"LN(J)$
BETA..
G(J.XI=I$
IF RN(XI NEO J$
BEGIN
X=RNIX)$
GO TO BETAS
END$ END", END$
COMMENT
THIS FiNDS THtO SIGIJ) VECTO~S BY SUM .. ING THt: GIJ . . RO"'S$
MU ••
FOR J = I I • I • JM I $
BEGIN
SIGIJI = 0$
FOR I = I I • I • JM) $
SIG(JI = SIG(JI + GIJ.I 1$
END$
COMMENT
THIS FINDS SMALLEST J FOR WHICH SU"I GIJ.I )K( I)
SIG(J).
AND FOR WHI CH K EOUALS O. AND COMPUTES
DELTA..

DON ••

I I'"

([NIPJ)

MIJ)=I$
NIJ )=C I JI$
FIJI=2$

1("'.

COMMENT

AND

KPIJ)=I$
K (JI=I$
MIJ)=I$
GIJ.J)=I$
N IJ I=C(~I)$
F(JI=O$
R I J I = [ 1'.1 I SJ 1$
FOR KA=II.I.JM)$
BEG[N
[F BIKAI EOL RIJ)$
RN(J)=KA$
END$
END$
IINISJ) NEQ 24000000CO) AND I [N(PJ) EOL 2300000000)$
BEGIN
FIJ)"'I$
R IJ I=[N (SJ) $
FOR KA=(!.I.JMI$
BEGIN
IF BIKAI EOL R(JI$
RN(J)=KA$
!F BCKA) EOL LIJ)$
LNIJI : KA$

COMMENT
THIS PROGRAM TAKES A GENERALIZED DATA STRUCTURE FIELD
AS I NPUT AND GENERA TES A T ABLE UPON '""H I CH THE GENt:"AL I ZED
LINEAR STORAGE MAPPlt-.G FUNCTION OPE"ATES.TrlE INPUT
REQln RES EAC~YMSOL rN THE F I Ei...D TO 8E ON A SEPARA rE CARl.)
CODED IN THE B220 ALPHANUMERIC CODF. IOACH IDE"ITIFIER AND
INl:EGER MUST BE ONE
CHARACTEP LONG. LET THIO NU""8EQ CF
CARDS "lE
'$
GIVEN THE INPUT FIELD. THE OUTPUT WILL 8::: IN THE
FORM
OF A TABLE
WITH 01£ ROW FOR EACH IDENl/lTIFIt::R. THESE
ARE LISTED UNDER
THE HEADING BIJ). THE OTHER COLUMNS
ARE J,' FeJ). LC')i, ~(..J). CC,J), N(J), M(..)}. AND Q ( J ) .

SJ=SIJI+I$
PJ=PIJ)+3$
!IN(SJ) NF:Q 24000:J0000I
BEG[N

EOL

M (J) AND N (J I.
REPEATS UNT IL NO J.S REMA IN$
FOR J=lloI.J",)$
BEGIN
TAUIJI=O$
FOR 1= lIo1.JM)$
TAUIJ)=TAUIJl+GIJ.1 I.KI 11$
END$
IY=O$
FOR I = I I • I • J" I $
BEGIN
IF ITAUIII EOL SIGIllI AND (KIll EOL 01$
BEGIN
[Y

Mil 1=0$
FOR ! X = {~. 1 i JM }"
"I I )=011 I I+GI I.IX).NI IX)$
N I I I =C I I )0'" I I ) $
K( I 1=1$
ENDS
END$
IF IY EOL 1$
GO TO DEL TA$
COM~ENT
TH! 5 CQMPUTES Q VECTO~ $
o I I) = 0$
1=1 $
EPSILON . .
IF I F I l l EOL 0) OR I F l t l EOL 21$

DATA STRUCTURES THAT GENERALIZE RECTANGULAR ARRAYS
BEGIN
IF I EOL JM$
GO TO PUTOUT$
I = 1+1 $
GO TO EPS 11..0N$
END$
Q(l..N( I 1 1=0$
IV=l..N" ) $
ZETA..
IF RNCIVI EQl.. 1$
BEGIN
IF I EQl.. JM$
GO TO PUTOUT$

I
1+1$
GO TO EPSll..ON$
END $
Q(RNC IV) 1 = "I ( IV) + Q( IV)$
IV = RN( IV)$
GO TO ZETA$
PUTOUT..
WRITE($$ HEAD)$
IMR!TE 1$$ TA8.L~~FORM)$
COMMENT
AT TH I S PO I NT THE PROGRAM \0 I l..l.. ACCEPT
REFERENCE
EXPRESSIONS IN THE FORM IDENTIFIER. INTEGER. IDENTIFIER.
INTEGER ETC. EACH IS ON
A SEPARATE CARD AND Al..PHANUMERICAl..l..Y CODED. THEy MUST BE PRECEDED BY A CARD
CONTA I N I NG TZ. THE NUMBER OF CARDS 1 N THE
REFERENCE EXPRESS 1 ON$
INPUT
TESTCTZ.FOR I=CI.I.TZ)$T(I»$
OUTPUT
POS IT ION (SMF) 'I>
FORMA T
POS ( I I
wo 1 $
TESTSTART ••
READ
C$$TEST)$
FOR 1=( I • I • TZ/2 ) $
BEGIN
T<21 )=CT(21 )-80000000001/ICOOOOOOO$
FOR J=(I" .JM)!f.
BEGIN
IF B(JI EQl.. T(21-1 1$
TNC I ) =J$
END$
END$
THIS IS THE STORAGE MAPPING FUNCTION COMPUTATION$
COMMENT

°.

FOR 1=(I.I.TZ/2I$
SMF=SMF+M (TN ( 1 ) I. (T (21 )-1 ) +0 (TN ( 1 ) )$

THFEND ••

WR ITE
($$POS IT I ON.POS) $
GO TO TESTSTART$
FINISH$

333

335

AN EXPERIMENTAL TIME-SHARING SYSTEM
Fernando J. Corbato, Marjorie Merwin-Daggett, Robert C. Daley
Computer Center, Massachusetts Institute of Technology
Cambridge, Massachusetts

summary
It is the purpose of this paper to discuss
briefly the need for time-sharing, some of the
implementation problems, an experimental timesharing system which has been developed for the
contemporary IBM 7090, and finally a scheduling
algorithm of one of us (FJC) that illustrates
some of the techniques which may be employed to
enhance and be analyzed for the performance
limits of such a time-sharing system.

Introduction
The last dozen years of computer usage have
seen great strides. In the early 1950's, the
problems solved were largely in the construction
and maintenance of hardware; in the mid-1950's,
the usage languages were greatly improved with
the advent of compilers; now in the early 1960's,
we are in the midst of a third major modification to computer usage: the improvement of
man-machine interaction by a process called
time-sharing.
Much of the time-sharing philosophy,
expressed in this paper, has been developed in
conjunction wi th the work of an MIT preliminary
study committee, chaired by H. Teager, which
examined the long range computational needs of
the Institute, and a subsequent MIT computer
working committee, chaired by J. McCarthy.
However, the views and conclusions expressed
in this paper should be taken as solely those
of the present authors.
Before proceeding further, it is best to
give a more precise interpretation to timesharing. One can mean using different parts of
the hardware at the same time for different
tasks, or one can mean several persons making
use of the computer at the same time. The first
___
Tn,,' +;
n('l'
; c::
meAning, VoL,",,"","''''
" ' - .......... '"" .... _ - .... -l""' .. - b .. - .. • ... · _ ..... b '
-oriented towards hardware efficiency in the
sense of attempting to a~t~i9 §omplete utilization of all components ' , J • The second
meaning of time-sharing, which is meant here,
is primarily concerned with the efficiency of
persons trying to use a computer l ,2,3,4.
Computer efficiency should still be considered
but only in the perspective of the total system
utili ty.
_~+

T\.,.,.nty,...~mm;

The motivation for time-shared computer
usage arises out of the slow man-computer interaction rate presently possible with the bigger,
more advanced computers. This rate has changed
little (and has become worse in some cases) in
the last decade of widespread computer use. lO
In part, this effect has been due to the
fact that as elementary problems become mastered on the computer, more complex problems
immediately become of interest. As a result,
larger and more complicated programs are written
to take advantage of larger and faster computers.
This process inevitably leads to more programming errors and a longer period of time required
for debugging. Using current batch monitor
techniques, as is done on most large computers,
each program bug usually requires several hours
to eliminate, if not a complete day. The only
alternative presently available is for the
programmer to attempt to debug directly at the
computer, a process which is grossly wasteful
of computer time and hampered seriously by the
poor console communication usually available.
Even if a typewriter is the console, there are
usually lacking the sophisticated query and
response programs which are vitally necessary
to allow effective interaction. Thus, what is
desired is to drastically increase the rate of
interaction between the programmer and the
computer without large economic loss and also
to make each interaction more meaningful by
extensive and complex system programming to
assist in the man-computer communication.
To solve these interaction problems we
would like to have a computer made simultaneously
available to many users in a manner somewhat
like a telephone exchange. Each user would be
able to use a console at his own pace and without concern for the activity of others using the
Q'l:Tc+om

-,J -

- _ ........

This console could as a

~~nimum

merely a typewriter but more ideally would
contain an incrementally modifiable selfsustaining display. In any case, data transmission requirements should be such that it would
be no major obstacle to have remote installation
from the computer proper.

336

The basic technique for a time-sharing system
is to have many persons simultaneously using the
computer through typewriter consoles with a
time-sharing supervisor program sequentially
running each user program in a short burst or
quantum of computation. This sequence, which in
the most straightforward case is a simple roundrobin, should occur often enough so that each
user program which is kept in the high-speed
memory is run for a quantum at least once during
each approximate human reaction time (~.2
seconds). In this way, each user sees a computer
fully responsive to even single key strokes each
of which may require only trivial computation;
in the non-trivial cases, the user sees a
gradual reduction of the response time which is
proportional to the complexity of the response
calculation, the slowness of the computer, and
the total number of active users. It should be
clear, however, that if there are n users
actively requesting service at one time: each
user will only see on the average lin of the
effective computer speed. During the period of
high interaction rates while debugging programs,
this should not be a hindrance since ordinarily
the required amount of computation needed for
each debugging computer response is small
compared to the ultimate production need.
Not only would such a time-sharing system
improve the ability to program in the conventional
manner by one or two orders of magnitude, but
there would be opened up several new forms of
computer usage. There would be a gradual
reformulation of many scientific and engineering
applications so that programs containing decision
trees which currently must be specified in
advance would be eliminated and instead the
particular decision branches would be specified
only as needed. Another important area is that
of teaching machines which, although frequently
trivial computationally, could naturally
exploit the consoles of a time-sharing system
with the additional bonus that more elaborate
and adaptive teaching programs could be used.
Finally; as attested hy the many small business
computers, there are numerous applications in
busine$ and in industry where it would be
advantageous to have powerful computing facilities
available at isolated locations with only the
incremental capital investment of each console.
But it is important to realize that even \rithout
the above and other new applications, the major
advance in programming intimacy available from
time-sharing would be of immediate value to
computer installations in universities, research
laboratories, and engineering firms where
program debugging is a major problem.

PROGRA~tMING

AND CODING

Implementation Problems
As indicated, a straightforward plan for
time-sharing is to execute user programs for
small quantums of computation without priority
in a simple round-robin; the strategy of timesharing can be more complex as will be shown
later, but the above simple scheme is an
adequate solution. There are still many
problems, however, some best solved by hardware, others affecting the programming conventions and practices. A few of the more
obvious problems are summarized:
Hardware Problems:
1. Different user programs if simultaneously in core memory may interfere with each
other or the supervisor program so some form of
memory protection mode should be available when
operating user programs.
2. The time-sharing supervisor may need
at different times to run a particular program
from several locations. (Loading relocation
bits are no help since the supervisor does not
know how to relocate the accumulator, etc.)
Dynamic relocation of all memory accesses that
pick up instructions or-data words is one
effective solution.
3. Input-output equipment may be initiated
by a user and read words in on another user
program. A way to avoid this is to trap all
input-output instructions issued by a user's
program when operated in the memory protection
mode.
4. A large random-access back-up storage
is desirable for general program storage files
for all users. Present large capacity disc
units appear to be adequate.
5. The time-sharing supervisor must be
able to interrupt a user's program after a
quantum of computation. A program-initiated oneshot multivibrator which generates an interrupt
a fixed time later is adequate.
6. Large core memories (e.g. a million
words) would ease the system programming complications immensely since the different active
user programs as well as the frequently used
system programs such as compilers, query programs,
etc. could remain in core memory at all times.
programming Problems:
1. The supervisor program must do automatic user usage charge accounting. In general,

337

AN EXPERIMENTAL TIME-SHARING SYSTEM

the user should be charged on the basis of a
system usage formula or algorithm which should
include such factors as computation time, amount
of high-speed memory required, rent of secondary
memory storage, etc.
2. The supervisor program should coordinate
all user input-output since it is not desirable
to require a user program to remain constantly
in memory during input-~utput limited operations.
In addition, the supervisor must coordinate all
usage of the central, shared high-speed inputoutput units serving all users as well as the
clocks, disc units, etc.
3. The system programs available must be
potent enough so that the user can think about
his problem and not be hampered by coding
details at'typographical mistakes. Thus,
compilers, query programs, post-mortem programs,
loaders, and good editing programs are
essential.
4. As much as possible, the users should
be allowed the maximum programming flexibility
both in choices of language and in the absence
of restrictions.

Usage Problems
1. Too large a computation or excessive
typewriter output may be inadvertently requested
so that a special termination signal should be
available to the user.

2. Since real-time is not computer usagetime, the supervisor must keep each user informed
so that he can use his judgment regarding loops,
etc.
3. Computer processor, memory and tape
malfunctions must be expected. Basic operational
questions such as "Which program is running?"
must be answerable and recoveIYprocedures fully
anticipated.

An Experimental Time-Sharing System for the IBM
7090
Having briefly stated a desirable timesharing performance, it is pertinent to ask
what level of performance can be achieved with
existant equipment. To begin to answer this
question &nd to explore all the programming and
operational aspects, an experimental timesharing system has been developed. This system
was originally written for the IBM 709 but has
since been converted for use with the 7090
computer.

The 7090 of the MIT Computation Center has,
in addition to three channels with 19 tape units,
a fourth channel with the standard Direct Data
Connection. Attached to the Direct Data Connection is a real-time equipment buffer and control
rack designed and built* under the direction of
H. Teager and his group. This rack has a variety
of devices attached but the only ones required
by the present systems are three flexowriter
typewriters. Also installed on the 7090 are two
special modifications (i.e. RPQ's): a standard
60 cycle accounting and interrupt clock. and a
special mode which allows memory protection,
dynamic relocation and trapping of all user
attempts to initiate input-output instructions.
In the present system the time-sharing
occurs between four users, three of whom are online each at a typewriter in a foreground
system, and a fourth passive user of the background Fap-Mad-Madtran-BSS Monitor System similar
to the Fortran-Fap-BSS Monitor System (FMS) used
by most of the Center programmers and by many
other 7090 installations.
Significant design features of the foreground system are:
1. It allows the user to develop programs
in languages compatible with the background
system,

Develop a private file of programs,

3. Start debugging sessions at the state
of the previous session, and

4. Set his own pace with little waste of
computer time.

Core storage is allocated such that all users
operate in the upper 27,000 words with the timesharing supervisor (TSS) permanently in the
lower 5,000 words. To avoid memory allocation
clashes, protect users from one another, and
simplify the initial 709 system organization,
only one user was kept in core memory at a
time. However, with the special memory protection and relocation feature of the 7090, more
sophisticated storage allocation procedures are
being implemented. In any case, user swaps are
minimized by using 2-channel overlapped magnetic
tape reading and writing of the pertinent
locations in the two user programs.
The foreground system is organized around
commands that each user can give on his typewriter and the user's private program files
which presently (for want of a disc unit) are
kept on a separate magnetic tape for each user.

This group is presently using another approach 9
in developing a time-sharing system for the
MIT 7090.

338
For convenience the format of the private tape
files is such that they are card images. have
title cards with name and class designators and
can be written or punched using the off-line
equipment. (The latter feature also offers a
crude form of large-scale input-output.) The
magnetic tape requirements of the system are the
seven tapes required for the normal functions of
the background system. a system tape for the
time-sharing supervisor that contains most of
the command programs. and a private file tape
and dump tape for each of the three foreground
users.
The commands are typed by the user to the
time-sharing supervisor (not to his own program)
and thus can be initiated at any time regardless
of the particular user program in memory. For
similar coordination reasons. the supervisor
handles all input-output of the foreground
system t)vewriters. Co~~~nds are composed of
segments separated by vertical strokes; the
first segment is the command name and the
remaining segments are parameters pertinent to
the command. Each segment consists of the last
6 characters typed (starting vdth an implicit
6 blanks) so that spacing is an easy way to
correct a typing mistake. A carriage return is
the signal which initiates action on the command.
Whenever a command is received by the supervisor,
"WAIT". is typed back followed by .. READY." when
the command is completed. (The computer responses
are always in the opposite color from the user's
typing.) While typing. an incomplete command
line may be ignored by the "quit" sequence of a
code delete signal followed by a carriage return.
Similarly after a command is initiated. it may
be abandoned if a "quit" sequence is given. In
addition, during unwanted command typeouts, the
command and output may be terminated by pushing
a special "stop output" button.
The use of the foreground system is initiated
whenever a typewriter user completes a command
line and is placed in a waiting command queue.

PROGRAMMING AND CODING

Whenever the waiting command queue is
empty, the supervisor proceeds to execute a
simple round-robin of those foreground user
programs in the working status queue. Finally,
if both these queues are empty, the background
user program is brought in and run a quantum at
a time until further foreground system actively
develops.
Foreground user programs leave the working
status queue by two means. If the program
proceeds to completion, it can reenter the
supervisor in a way which eliminates itself and
places the user in dead status; alternatively,
by a different entry the program can be placed
in a dormant status (or be manually placed by
the user executing a quit sequence). The dorw~nt
status differs from the dead status in that the
user may still restart or examine his program.
User input-output is throu~h each typewriter, and even though the supervisor has a
few lines of buffer space available, it is
possible to become input-output limited.
Consequently, there is an additional inputoutput wait status, similar to the dormant,
which the user is automatically placed in by
the supervisor program whenever input-output
delays develop. When buffers become near
empty on output or near full on input, the user
program is automatically returned to the working
status; thus waste of computer time is avoided.

Commands
To clarify the scope of the foreground
system and to indicate the basic tools available to the user. a list of the important
commands follows along with brief summaries of
their operations:
1.

Ia
a

= arbitrary

UPOil conlplet1on. of each quantlliu. J the time..:sharing

supervisor gives top priority to initiating any
waiting commands. The system programs corresponding to most of the commands are kept on the
special supervisor command system tape so that to
avoid waste of computer time, the supervisor
continues to operate the last user program until
the desired command program on tape is positioned
for reading. At this point, the last user is
read out on his dump tape, the command program
read in, placed in a working status and initiated
as a new user program. However, before starting
the new user for a quantum of computation, the
supervisor again checks for any waiting command
of another user and if necessary begins the lookahead positioning of the command system tape
while operating the new user.

a
~

text treated as a comment.

Ia I~

user problem number
user programmer number

Should be given at beginning of each
user's session. Rewinds user's private file tape;
clears time accounting records.
3.

logout

Should be given at end of each user's
session. Hewinds user's private file tape;
punches on-line time accounting cards.
4.

input

Sets user in input mode and initiates
auto~~tic generation of line numbers.
The user

3.39

AN EXPERIMENTAL TIME-SHARING SYSTEM

types a card image per line according to a
format appropriate for the programming language.
(The supervisor collects these card images at
the end of the user's pri va te file tape.) When
in the automatic input mode, the manual mode may
be entered by giving an initial carriage return
and typing the appropriate line number followed
by
and line for as many lines as desired. To
reenter the automatic mode, an initial carriage
return is gi ven •

The manual mode allows the user to overwrite previous lines and to insert lines. (cf.
File Command.)
5.

Ia I

edit

a
p

title of file
class of file

The user is set in the automatic input
mode with the designated file treated as initial
input lines. The same conventions apply as to
the input command.
6.

Ia Ip

file
a

= ti tie

The created file will consist of the
numbered input lines (i.e. those at the end of
the user's private file tape) in sequence; in
the ~ase of duplicate line numbers, the last
version will be used. The line numbers will be
written as sequence numbers in the corresponding
card images of the file.
For convenience the following editing
conventions apply to input lines:
a. an underline signifies the deletion of
the previous characters of the line.
b. a backspace signifies the deletion of
the previous character in the field.
The following formats apply:
a. FAP: symbol, tab, operation, tab,
variable field and comment.
b. MAD, MAIYrRAN, FORTHAN: statement label,
tab, statement. To place a character in the
continuation column: statement label, tab,
backspace, character, statement.
~TA:

fap

mad

causes file a,mad to be translated by
the MADtranslator (compiler). File a,bss is
created.
9.

madtrn

cols. 1-72.

Causes the file designated as a, fap to
be translated by the FAP translator (assembler).
Files a, symtb and a,bss are added to the user's
private file tape giving the symbol table and
the relocatable binary BSS form of the file.

causes file a,madtrn (i.e. a pseudoFortran language file) to be edited into an
equivalent file a,mad (added to the user's file)
and translation occurs as if the command madla
had been given.
10.

load

I a 1 ••• la
2
l
n
causes the consecutive loading of files
O1,bss (i=1,2, ••• ,n). An exception occurs if 01=
(libe), in which case file a. ,bss is searched
~+l
as a library file for all subprograms still
missing. (There can be further library files.)
I

1···1

use
al
a2
an
This command is used whenever a load or
previous use command notifies the user of an
incomplete set of subprograms. Same a. conventions as for load.
~
11.

to be given to file

p = class of language used during input

12.

start

Ia I

Starts the program setup by the load
and use commands (or a dormant program) after
first positioning the user private file tape in
front of the title card for file a,p. (If p is
not given, a class of data is assumed; if both
a and p are not given, no tape movement occurs
and the program is started.)
13.

pm I a
a = "lights", "stomap", or the usual

format of the standard Center post-mortem (F2PM)
request: subprogram name
loc
loc
mode
.
.
1
2
d ~rect~on where mode and direction are optional.

Produces post-mortem of user's dormant
program according to request specified by a.
(E.g. matrix
5
209
flo
rev will cause to
be printed on the user's typewriter the contents
of subprogram "matriX" from relative locations
5 to 209 in floating point form and in reverse
sequence.)

14.

skippm

Used if a pm command is "quit" during
output and the previous program interruption is to
be restarted.
15.

listf

Types out list of all file titles on
user's private file tape.

340

PROGRAMMING AND CODING

16.

printf

Ia I~ I

Types out file a,~ starting at line
number y. If Y is omitted, the initial line is
assumed. Whenever the user's output buffer fills,
the command program goes into an liO wait status
allowing other users to time-share until the
buffer needs refilling.
17.

xdump

Ia I~

Creates file a,~ (if ~ omitted, xdump
assumed) on user's private file tape consisting
of the complete state of the user's last dormant
program.
18.

xdump

Ia I

Inverse of xdump command in that it
resets file a,~ as the user's program, starting
it where it last left off.
Although experience with the system to date
is quite limited, first indications are that
programmers would readily use such a system if it
were generally available
It is useful to ask,
now that there is some operating experience with
the 7090 system, what observations can be made.
An immediate comment is that once a user gets
accustomed to computer response, delays of even
a fraction of a minute are exasperatingly long,
an effect analogous to conversing with a slowspeaking person. Similarly, the requirement that
a complete typewritten line rather than each
character be the minimum unit of man-computer
communication is an inhibiting factor in the
sense that a press-to-talk radio-telephone conversation is more stilted than that of an
ordinary telephone. Since maintaining a rapid
computer response on a character by character
basis requires at least a vestigial response
program in core memory at all times, the straightforward solution within the present system is to
have more core memory available. At the very
least, an extra bank of memory for the timesharing supervisor would ease compatibility problems with programs already written for 32,000
word 7090's.
For reasons of expediency, the weakest
portions of the present system are the conventions
for input, editing of user files, and the degree
of rapid interaction and intimacy possible while
debugging. Since to a large extent these areas
involve the taste, habits, and psychology of the
users, it is felt that proper solutions will
require considerable experimentation and pragmatic evaluation; it is also clear that these
areas cannot be treated in the abstract for the
programming languages used will influence greatly
the appropriate techniques. A greater use 6f
symbolic referencing for locations, program names
and variables is certainly desired; symbolic postmortem programs, trace programs, and before-andafter differential dump programs should play
useful roles in the debugging procedures.

In the deSign of the present system, great
care went into making each user independent of
the other users. However, it would be a useful
extension of the system if this were not always
the case. In particular, when several consoles
are used in a computer controlled group such as
in management or war games, in group behavior
studies, or possibly in teaclting machines, it
would be desirable to have all the consoles
communicating with a single program.
Another area for further improvement within
the present system is that of file maintenance,
since the presently used tape units are a hindrance to the easy deletion of user program files.
Disc units will be of help in this area as well
as with the problem of consolidating and
scheduling large-scale central input-output
generated by the many console users.
Finally, it is felt tr~t it would be desir~
able to have the distinction between the foreground and background systems eliminated. The
present-day computer operator would assume the
role of a stand-in for the background users,
using an operator console much like the other
user consoles in the system, mounting and demounting magnetic tapes as requested by the
supervisor, receiving instructions to read card
decks into the central disc unit, etc. Similarly
the foreground user, when satisfied with his
program, would by means of his console and the
supervisor program enter his program into the
queue of production background work to be
performed. With these procedures implemented
the distinction of whether one is time-sharing
or not would vanish and the computer user would
be free to choose in an interchangable way that
mode of operation which he found more suitable
at a particular time.

A Multi-LeVel Scheduling Algorithm
Regardless of whether one has a million
word CQre memory or a 32: 000 word memory as
currently exists on the 7090, one is inevitably
faced with the problem of system saturation
where the total size of active user programs
exceeds that of the high-speed memory or there
are too many active user programs to maintain
an adequate response at each user console.
These conditions can easily arise with even a
few users if some of the user programs are
excessive in size or in time requi~ements. The
predicament can be alleviated if it is assumed
that a good design for the system is to have a
saturation procedure which gives graceful degradation of the response time and effective
real-time computation speed of the large and
long-running users.

AN EXPERIMENTAL TIME-SHARING SYSTEM

341

To show the general problem, Figure I
qualitatively gives the user service as a function
of n, the number of active users. This service
parameter might be either of the two key factors:
computer response time or n times the real-time
computation speed. In either case there is some
critical number of active users, N, representing
the effective user capacity, which causes saturation. If the strategy near saturation is to
execute the simple round-robin of all users, then
there is an abrupt collapse of service due to the
sudden onset of the large amount of time required
to swap programs in-and-out of the secondary
memory such as a disc or drum unit. Of course,
Figure I is quite qualitative since it depends
critically on the spectrum of user program sizes
as well as the spectrum of user operating times.

Similarly, if a program of size w at level

t, during operation requests a change fn memory
size from the time-sharing supervisor, then the
enlarged (or reduced) version of the program
should be placed at the end of the £tI queue where

t" = £ + [ log2 (

[=:J J·
+1)

(2)

Again the process is re-initiated with the headof-the-queue user at the lowest occupied level
of £'.
Several important conclusions can be drawn
from the above algori thm which allow the performance of the system to be bounded.
Computational Efficiency

To illustrate the strategy that can be employed to improve the saturation performance
of a time-sharing system, a multi-level scheduling algorithm is presented. This algorithm also
can be analyzed to give broad bounds on the
system performance.
The basis of the multi-level scheduling
algorithm is to assign each user program as it
enters the system to be run (or completes a
response to a user) to an £th level priority
queue. Programs are initially entered into a
level £0' corresponding to their size such that
£0

= [10g2

( [ :: ] + 1 ) ]

(1)

where w is the number of words in the program,
w is tge number of words which can be transm~tted in and out of the high-speed memory from
the secondary memory in the time of one quantum,
q, and the bracket indicates "the integral part
of". Ordinarily the time of a quantum, being
the basic time unit, should be as small as
possible without excessive overhead losses when
the supervisor switches from one program in highspeed memory to another. The process starts with
the time-sharing supervisor operating the program
at the head of the lowest level occupied queue,
£, for up to 2£ quanta of time and then if the
program is not completed (i.e. has not made a
response to the user) placing it at the end of
the £+1 level queue. If there are no programs
entering the system at levels lower than £, this
process proceeds until the queue at level £ is
exhausted; the process is then iteratively begun
again at level £+1, where now each program is
run for 2£+1 quanta of time. If during the
execution of the 2£ quanta of a program at level
£, a lower level, t', becomes occupied, the
current user is replaced at the head of the £th
queue and the process is reinitiated at level

tt.

1. Because a program is always operated for
a time greater than or equal to the swap time
(i.e. the time required to move the program in
and out of secondary memory), it follows that
the computational efficiency never falls below
one-half. (Clearly, this fraction is adjustable
in the formula for the initial level, to.) An
alternative way of Viewing this bound is to say
that the real-time computing speed available to
one out of n active users is no worse than if
there were 2n active users all of whose programs
were in the high-speed memory.
Response Time
2. If the maximum number of active users
is N, then an individual user of a given program
size can be guaranteed a response time,
tr

~ 2Nq[ :: ] + 1)

(3)

since the worst case occurs when all competing
user programs are at the same level. Conversely,
if tr is a guaranteed response of arbitrary
value and the largest size of program is assumed,
then the maximum permissible number of active
users is bounded.
Long Runs
3. The relative swap time on long runs can
be made vanishingly small. This conclusion
follows since the longer a program is run, the
higher the level number it cascades to with a
correspondingly smaller relative swap time. It
is an important feature of the algorithm that long
runs must in effect prove they are long so that
programs which have an unexpected demise are
detected quickly. In order that there be a
finite number of levels, a maximum level number,
L, can be established such that the asymptotic
swap overhead is some arbitrarily small
percentage, p:

342

PROGRAMMING AND CODING

L [lOg2

([:~~XJ

+1)]

(4)

where w
is the size of the largest possible
pmax
program.
Mul ti-Ievel vs. Single-level Response Times
4. The response time for programs of equal
size. entering the system at the same time. and
being run for multiple quanta. is no worse than
approximately twice the response-time occurring
in a single quanta round-robin procedure. If
there are n equal sized programs started in a
queue at level t. then the worst case is that of
the end-of-the-queue program which is ready to
respond at the very first quantlli~ r~~ at the
£+j level. Using the multi-level algorithm. the
total delay for the end-of-the-queue program is
by virtue of the geometric series of quanta:
Tm'- q2.e {n(2j -l) + (n-l) 2

(5)

Since the e~d-qf-the-queue user has computed for
a time of 2 (2 J -l) quanta, the equivalent singlelevel round-robin delay before a response is:
(6)

Hence
1

n-l) (2j
+ ( ----.--- )
n

2J-I

(7)

and the assertion is shown. It should be noted
that the above conditions. where program swap
times are omitted. which are pertinent when all
programs remain in high-speed memory. are the
least favorable for the multi-level algorithm; if
swap times are included in the above analysis, the
ratio of Tm I Ts can only become smaller and may
become much less than unity. By a similar analysis
it is easy to show that even in the unfavorable
case where there are no program swaps. head-of-thequeue programs that terminate just as the 2 t +j
quanta are completed receive under the multilevel algorithm a response which is twice as
fast as that under the single-level round-robin

m IT s = 1/2).

(Le. T

Highest Serviced Level
5. In the multi-level algorithm the level
classification procedure for programs is entirely
automatic, depending on performance and program
size rather than on the declarations (or hopes)
of each user. As a user taxes the system. the
degradation of service occurs progressively
starting with the higher level users of either
large or long-running programs; however, at some
level no user programs may be run because of too
many active users at lower levels. To determine

a bound on this cut-off point we consi~er N
active users at level £ each running 2 quanta,
terminating, and reentering the system again at
level £ at a user response time, t u ' later. If
there is to be no service at level £+1, then the
computing time, Nq2£, must be greater than or
equal to tu. Thus the guaranteed active levels,
.e , are given by the relation:
a
.ea

[ log2 (tu)
Nq

1
J

(8)

In the limit, tu could be as small as a minimum
user reaction time (~.2 sec.), but the expected
value would be several orders of magnitude
greater as a result of the statistics of a
large number of users.
The multi-level algorithm as formulated
above makes no explicit consideration of the seek
or latency time required before transmission of
programs to and from disc or drum units when
they are used as the secondary memory, (although
formally the factor Wq could contain an average
figure for these times). One simple modification
to the algorithm which usually avoids wasting
the seek or latency time is to continue to
operate the last user program for as many quanta
as are required to ready the swap of the new user
with the least priority user; since ordinarily
only the higher level number programs would be
forced out into the secondary memory. the
extended quanta of operation of the old user
while seeking the new user should be but a minor
distortion of the basic algorithm.
Further complexities are possible when the
hardware is appropriate. In computers with inputoutput channels and low transmission rates to and
from secondary memory, it is possible to overlap
the reading and writing of the new and old users
in and out of high-speed memory while operating
the current user. The effect is equivalent to
using a drum giving 100 % multiplexor usage but
there are two liabilities, namely. no individual
user can utilize all the available user memory
space and the look-ahead procedure breaks down
whenever an unanticipated scheduling change
occurs (e.g. a program terminates or a higherpriority user program is initiated).
Complexity is also possible in storage
allocation but certainly an elementary procedure
and a desirable one with a low-transmission rate
secondary memory is to consolidate in a single
block all high-priority user programs whenever
sufficient fragmentary unused memory space is
available to read in a new user program. Such a
procedure is indicated in the flow diagram of the
multi-level scheduling algorithm which is given
as Figure 2.

AN EXPERIMENTAL TIME-SHARING SYSTEM

343

It should also be noted that Figure 2 only
accounts for the scheduling of programs in a
working status and still does not take into
account the storage allocation of programs which
are in a dormant (or input-output wait status).
One systematic method of handling this case is
to modify the scheduling algorithm so that
programs which become dormant at level £ are
entered into the queue at level £+1. The
scheduling algorithm proceeds as before with the
dormant programs continuing to cascade but not
operating when they reached the head of a queue.
Whenever a program must be removed from highspeed memory, a program is selected from the endof-the-queue of the highest occupied level
number.
Finally, it is illuminating to apply the
multi-level scheduling algorithm bounds to the
contemporary IBM 7090. The following approximate
values are obtained:
q = 16 m.s. (based on 1% switching overhead)
Wq = 120 words (based on one IBM 1301 model
2 disc unit without seek or latency
times included)
tr

BNf

£a

10g2 (lOOO/N) (based on tu = 16 sec.)

£0

B (based on a maximum program size of

(based on programs of (32k)f
sec. words)

32K words)
Using the arbitrary criteria that programs
up to the maximum size of 32,000 words should
always get some service, which is to say that
max la= max £0 ' we deduce as a conservative
estimate that N can be 4 and that at worst the
response time for a trivial reply will be 32
seconds.
The small value of N arrived at is a direct
consequence of the small value of Wq that results
from the slow disc word transmission rate. This
rate is only 3.3% of the maximum core memory
multiplexor rate. It is of interest that using
high-capacity high-speed drums of current design
such as in the Sage System of in the IBM Sabre
System it would be possible to attain nearly
100% multiplexor utilization and thus multiply
w by a factor of 30. It immediately follows
tgat user response times equivalent to those
_..: .... _ _ _ h - ... ,_ ... ...: .. l.. .. " ' _ ,.:1..; ..... _
•• _..: ...... _ ... ,...:1 h _ _ .... __
~

6 .....

Vw ... "

UOUVV":;;:

.,.. .... "".&..1.

"'.u.....

u ..... .,"'"

".•,u.........

WVU,.LU

Ut;;

O ....

VC.l.l

to 30 times as many persons or to 120 users; the
total computational capacity, however, would not
change.

In any case, considerable caution should be
used with capacity and computer response time
estimates since they are critically dependent
upon the distribution functions for the user
response time, t ' and the user program size,
u
wp , and the computational capacity requested by
each user. Past experience using conventional
programming systems is of little assistance because these distribution functions will depend
very strongly upon the programming systems made
available to the time-sharing users as well as
upon the user habit patterns which will gradually
evolve.
Conclusions
In conclusion, it is clear that contemporary
computers and hardware are sufficient to allow
moderate performance time-sharing for a limited
number of users. There are several problems
which can be solved by careful hardware design,
but there are also a large number of intricate
system programs which must be written before one
has an adequate time-sharing system. An important aspect of any future time-shared computer is
that until the system programming is completed,
especially the critical time-shal~ng supervisor,
the computer is completely worthless. Thus, it
is essential for future system design and implementation that all aspects of time-sharing system
problems be explored and understood in prototype
form on present computers so that major advances
in computer organization and usage can be made.

Acknowledgements
The authors wish to thank Bernard Galler,
Robert Graham and Bruce Arden, of the University
of Michigan, for making the ~1AD compiler available
and for their advice with regard to its adaption
into the present time-sharing system. The
version of the Madtran Fortran-to-Mad editor
program was generously supplied by Robert Rosin
of the University of Michigan. Of the MIT
Computation Center staff, Robert Creasy was of
assistance in the evaluation of time-sharing
performance, Lynda Korn is to be credited for her
contributions to the pm and madtran commands, and
Evelyn Dow for her work on the fap command.
T"t_-C _ _ _ • _ _ _ _

1l,1I;;:J,.t;;:.Lt;:11\,;t;:;:'

1. S trachey, C., "Time Sharing in Large
Fast Computers," Proceedings of the International
Conference on Information Processing, UNESCO
(June, 1959), Paper B.2.19.

PROGRAMMING AND CODING

344

6. Codd, E. F., "Multiprogram Scheduling,"
Communications of the ACM, 3, 6 (June, 1960),
347-350.

2. Licklider, J. C. R., "Man-Computer
Symbiosis," IRE Transactions on Human Factors in
Electronics, HFE-l, No.1 (March, 1960), 4-11.

3. Brown, G., Licklider, J. C. R.,
McCarthy, J., and PerIis, A., lectures given
spring, 1961, Management and the Computer of the
Future, (to be published by the M.I.T. Press,
March, 1962).

Heller, J., "Sequencing Aspects of

Mul tiprogramming," Journal of the ACM, 8, 3

(July, 1961), 426-439.
8. Leeds, H. D., Weinberg, G. M., "Multiprogramming," Computer Programming Fundamentals,
356-359, McGraw-Hill (1961).

4. Corbatc{, F. J .. , "An Experimental TimeSharing System," Proceedings of the IBM Uni versi ty
Director's Conference, July, 1961 (to be published) •

9. Teager, H. M., "Real-Time Time-Shared
Computer project," Communications of the ACM, 5,
1 (January, 1962) Research Summaries, 62.

5. Schmitt, W. F., Tonik, A. B., "Sympathetically programmed Computers~" Proceedings
of the International Conference on Information
processing, UNESCO, (June, 1959) Paper B.2.18.

10. Teager, H. M., McCarthy, J., "TimeShared Program Testing," paper delivered at the
14th National Meeting of the ACM (not published).

Quantum
finished

1
Any users
initiated
in level

£'<.1-

n·.)

= (J!

.L yes
Fut user
at end of
~+ 1 queue

Place current
user at head
of queue t.

,l-1'

Find head of

~------------------4~~e~~w~~~gram

Service

occupied leve
.l~

;\.

Is user at
head of queue
yes
in pri~ary
r---------------------------------------~
memory'?

.f0

n --;.

Figure 1.

Is there r)om
for head of
ves
queue program~------~~--------------~
in primary
memory'?

Service vs. Number of
Active Users

.is there
enough slack
in primary
memory for
urogram?
out
lowest
, priori ty
program

consolidate
slack.

Read in
program

read

Figure 2.

I
Flow Chart of Multi-Level Scheduling Algorithm

345

A PROGRAMMING LANGUAGE
Kenneth E. Iverson
Research Division, IBM Corporation
Yorktown Heights, New York

The paper describes a succinct problem-oriented programming language.
The language is broad in scope, having been developed for, and applied
effectively in, such diverse areas as microprogramming, switching theory,
operations research, information retrieval, sorting theory, structure of
compilers, search procedures, and language translation.
The language
permits a high degree of useful formalism.
It relies heavily on a systematic extension of a small set of basic operations to vectors, matrices,
and trees, and on a family of flexible selection operations controlled by
logical vectors.
Illustrations are drawn from a variety of applications.
1
The programming language outlined here
has been designed for the succinct description of
algorithms. The intended range of algorithms is
broad; effective applications include microprogramming, switching theory, operations research,
information retrieval, sorting theory, structure
of compilers, search procedures, and language
translation. The symbols used have been chosen
so as to be concise and mnemonic, and their
choice has not been restricted to the character
sets provided in contemporary printers and computers. A high degree of formalism is provided.

entities (e. g., numerals, alphabetic literals, or
logical variables) and R is any relation defined
upon them, then (x R y) is equal to 1 or 0 according to whether the relation R does or does not
ho ld between x and y. Thus (i = j) is the familiar
Kronecker de Ita cS ij> (ujv) is the exclusive or
function of the logical variables u and v, and
sgn x = (x > 0) - (x < 0)
is the familiar sign function, defined as +1, 0, or
-1 according as x is strictly positive, zero, or
strictly negative.
Vectors and Matrices

Basic Operations
The language is based on a consistent unification and extension of existing mathematica 1
notations, and upon a systematic extension of a
small set of basic arithmetic and logical operations to vectors, matrices, and trees. The
arithmetic operations include the four familiar
arithmetic operations and the absolute value
(denoted by the usual symbols) as well as the
floor, ceiling, and residue functions denoted and
defined as fo llows:

A vector is denoted by an underlined lowercase letter (e. g., x), its i-th component by x.,
and its dimension by v(~). A matrix is denot2
by an underlined uppercase letter (e. g., X), its
i-th row by ~~, its j-th column by ~j' its ij-th
element by X~, its row dimension (1. e., the
common diI~;nsion of its row vectors) by v(~),
and its column dimension by fl(~).
All of the basic operations are extended
component-by-component t9 vectors and matrices.
Thus,

Name

S}::mbol

floor

LXJ

Lxj ~ x

< Lxj

ceiling

rxl

rxl ~ x

> fxl

-1

_z = ~ X

residue mod m

min

Definition

n= mq

+ m I n;O,.::: m I n
Y <==>

= ~i

+ .Yi '

Zi = X~ X y~
-j
-]
-]

where LxJ, r xl, m, n, and q are integers.
The logical operations and, or, and not are
defined upon the logical variables Oand 1 and are
denoted by A, v, and an overbar. They are augmented by the re lational statement (proposition)
(x R y) defined as fo llows. If x and yare any

= (~<.Y) <===::>

The symbol,,: (n) will denote a logical vector £.f dimension n whose components are all unity,
and..: (n) therefore denotes the zero vector. The

346

PROGRAMMING AND CODING

(A B):

dimension n will be elided whenever it is clear
from context.
The cyclic left shift of a vector x is called
left rotation. It is denoted by k t x and defined
by the re lation:

:t.

where
is denoted by k

Right rotation
~ and is defined analogous ly.

For each basic binary operator 0, the 0reduction of a vector ~ is denoted by 0/~ anddefined by
= ( ••• (( _x 10 _x 2) 0 x ) 0 ••• 0 x
).
-3
-v(~)

Thus +/~ is the sum, and xix is the product of
all components of x. Moreove-;, if u = (1, 0, 1),
then +/!;!, = 2, +/~ =-1, AI!;!, = 0, and -VI!;!, = 1.
Reduction is extended to matrices row-byrow:
z

= 0/x
-

¢:::>

-1

= 0/x
-

and column-by-column:

= 0 I Ix
¢:::> z . = 0/x. ,
-1
-1

For example, if !;!, = (!;!'1' !;!, ) is a logical
vector of dimension two, then De ZMorgan' slaw
may be expressed as:

v/~

The reduction operation can be extended to
any relation R by substituting R for 0 in the formal definition above. The parentheses in the
definition now signify relational statements as
well as grouping, and thus the expression II!;!,
denotes the application of the exclusive-or over
all components of the logical vector u. For
example, 11(1,0,1) = ((1 10) I 1) = (1-;t 1) = O.
Induction can be used to show that

II!;!,= zl+/!;!" and = I!;!, = 21+/~.
Hence, I lu = =/~, a useful companion to

~= M ~ ~
defines the sense vector s of an associative .
memory such that ~i = 1 if and only if word M1
agrees with ~.

As further examples, R
P
Q give~ the
1
number of places in which a component of ~ exceeds the corresponding component of Q., and
~ = ~ ~ 9 is a "covering matrix" whi~:tl indicates
which rows of P cover (exceed in every component)
which rows of Q.

De Morgan's law and the identity

I I!;!, = =/u
establish a duality with respect to negation between A and v , and between I and =. This
dua lity is easily extended to matrices. For
example,
A ~ B

Selection
The formation of a vector .I from a vector
by deleting certain components of x will be
denoted by

= ~~,

where u is a logical vector (of dimension v (x) and
x. is d;leted if and only if u. = O. Thus u/;; and
TfJx provide a d isjoint deco~1position of x-: -;nd
T~ -;~) I ~ is the vector of all strictly po;Itive
components of ~.
The operation ~~ is called compression
and is extended to matrices by row and by column
as follows:

De Morgan's law.
Matrix Product

!:= ~

Thus C = M ~ X is an "incidence matrix"
such that Cr-= 1 if ;nd only if Mi and X. agree in
all componJnts. If M is the m-;mory ;-rla binary.
computer (i. e., M is a logical matrix and row M1
is the i-th word of memory), and if x is an
"argument register". then (treating ~ as a onecolumn matrix)

Moreover, this is the valid generalization of
De Morgan's law to a vector!;!, of arbitrary
dimension.

The conventional matrix product
be defined as:

where 0 and 02 are any operators or relations
1
with suitable domains.

the co luron reduction being distinguished by the
double slash.

AI!;!, =

-0 2 -

Reduction

o I_x

Adopting the notation A
B for this product makes
explicit the roles of th~ ba-;ic operations + and X,
and suggests the following useful generalization:
A

= (k t ~) <==>.Ii = ~ j ,
j = 1 + v (~) I (i + k - 1).

- - J

~
may

¢:::::>

Zi =

211~ ~ ~i

~~i
~~i·

A PROGRAMMING LANGUAGE

347

The familiar identity concerning partitioned
matrices can now be generalized as follows:

-x ~ -y

(u/X) ~ (u/ /Y)

- + (u/X)
-- ~ (u/
- /Y).
-

Since the identity depends only on the associativity
and commutativity of the operators + and X, it
holds also for all operators (and relations) possessing these properties. Moreover,

and

To illustrate other uses of compressioI?-'
consider a bank ledger l: so arranged that l:1
represents the i-th account, and l:1' l:2' and l:3
represent the vector'of names, of account num,bers, and of balances, respectively. Then the
preparation of a list ~ (in the same format) of all
accounts having a balance less than two dollars is
described by the statement:
P -

(L < 2 E
-3
-

) //

\~, ~, :e.\~ g/~ =~;
/~,~,:e.

Expansion: ~ = ~

<;:>

\:e. ~

~~ =

:e.

W~ = ~~; ~~ = ~2.
~ = \~,

~,:e.\

They may be extended to matrices in the established manner and are related by the obvious
identities:

:e.\
/~, ~, :e./

\~, ~,

where w is the weighting vector defined by
w ( ) =-1 and w. 1 = w. X V.' For example, if
-v w
-1- -1 """1
Y = (24, 60, 60) and if ~ = (I, 2, 5) is the elapsed
time in hours, minutes, and seconds, then
.:t. ~ = 3725 is the e lapsed time in seconds.

The value of x in a decimal system is denoted by (1 0 .:.)
~-; and in a binary system by
either (2 .:.) l~, or
~. Moreover, if y is any
real number, then (y .:.)
~ denotes the polynomia 1 in y with coefficients ~.

Application to Microprogramming

Three useful operations converse to compression are defined as follows:

Mask: z

If the components of the vector :t. specify the
radices of a mixed base number system and if x
is any numerical vector of the same dimension,then the value of x in that number system is
called the base y -;alue of x, is denoted by :t.l ~
and is defined formally by

L,
-

where the arrow denotes specification (in the
sense of the symbol = in Fortran and the symbol
.- in Algo 1).

Mesh: z =

Mixed Base Value

/lI\~' ~,
\~ /~, ~,

\:e. / ,
~/:e.\ .
~

To illustrate the use of the notation in describing the operation of a computer, consider the
IBM 7090 with a memory M of dimension 2 15 X 36,
a command vector .£ of di;;ension 36 representing
the instruction next to be executed, a sequence
vector s of dimension 15 representing the instruction cou-;'te r, and a 3 X 15 index matrix I representing the three index registers. The instruction
fetch phase of operation (excluding the channel
trap) can then be described as in Figure 1. 0 ~
origin indexing will be used for all vectors and
matric~e~s~.~______________________________~

£-Ml~

1~ -

2
1

a k

(~)

.£12

.£13

(18 + ~ 3) / .£

.!. _

(.£): 0

1 ~15 /.£ In addition to the full vector.:. {n} already
defined, it is convenient to define the prefix
vector ~j (n) as a logical vector of dimension n
whose first j components are unity. The suffix
vector wj (n) is defined analogous ly. An infix
vector ~ving i le~ding O's followed by j ~an
be denoted by i +~J. When used in compres sion
operations, these special vectors are very useful
in specifying fixed formats.

I (1 + 1 ~)

I (1 ~ 15 /.£ -1 (t XIn
=

~18 /.£ _ ~18 /Ml ~15/.£

Instruction Fetch of IBM 7090
Figure 1

PROGRAMMING AND CODING

348

Step 1 shows the selection of the next instruction from the memory word specified by the
instruction counter ~ and its transfer to the
command re giste r c. Step Z shows the inc re mentation (reduced ~odulo 2 15 ) of the counter s,
The logical function k 1 (c) of step 3 determineswhethe r the instruction J~st fetched be longs to the
class of instructions which are subject to indirect
addressing, the bits ~IZ and ,£13 determine
whether this particular instruction is to be
indexed, and a is therefore set to unity only if
indirect addressing is to be performed.
The function kZ(c) determines whether the
instruction is indexabl;. If kZ(c)
0, the branch
from step 4 to step 7 skips the potential indexing
of steps 5 and 6. As shown by step 6, indexing
proceeds by £!ing together the index registers
(i. e., rows of I) selected by the three tag bits
t = (18 ! a 3}/c,- subtracting the base two value of
the resulting ;ector from the address portion of

Or to storage

ORS

Or to accumulator

ORA

And to storage

ANS

And to accumulator

ANA

Exclusive or

ERA

to accumulator

Complement magnitude

COM

C lear magnitude

CLM

Change sign

CHS

Set sign plus

SSP

Set sign minus

SSM

Store logical word

SLW

Clear and add logical

CAL

Add and carry logical

ACL

the instruction c, reducing the result modulo Z15,
and respecifying the address portion of ~
accordingly.
The fetch terminates immediately from
step 7 if no indirect addressing is indicated;
otherwise step 8 performs the indirect addressing
and the indexing phase is repeated. Step 9 limits
the indirect addressing to a single level. It may
be noted that all format information is presented
directly in the microprogram.
The description of the execution phase of
computer operation will be illustrated by the
family of instructions for logical functions in the
7090. Representing the 38-bit accumulator by
the logical vector u (with v (u) = 38, and with
~, ~1' and ~Z rep~senting the sign, q and p bits,
respectively), these instructions may be de~
scribed as in Figure Zo

-0

Instructions in IBM 7090

Figure Z

A PROGRAMMING LANGUAGE

349

Ordered Trees
A tree can be represented graphically as in
Figure 3(a) and, since it is a special case of a
directed graph, it can also be represented by a
node vector ~ and connection matrix ~ as in
Figure 3(b).
Defining an ordered tree as a tree in which
the set of branches emanating from each node has
a specified ordering, a simple indexing sy·stem
for ordered trees can be defined in the manner
indicated by Figure 4(a). The dimension of the
vector index i assigned to each node is equal to
the number ofthe leve I on which it occurs. If T
is an ordered tree, then T. will denote the subtree rooted in the node witntindex .i. Thus T (1 1)
is the subtree enclosed in b.roken lines in
'
Figure 4(a). Moreover, T2. will denote the
(unique) path vector comprising all nodes from
the root to node i. Thus T (1, 2) = (a, b). The
maximum dimen;ion occurring among the index
vectors is called the height of the tree and is
denoted by v (T).
The index vector notation proves very convenient in describing algorithms involving tree
operands. Moreover, it provides a simple formalization of the two important representations
of a tree, the Lukasiewicz representation and the
level-by-level list.

If each index vector is augmented by
sufficient null components (denoted by 0) to bring
all to a common dimension equal to the height of
the tree, then they may all be arrayed in an
index matrix 1. as in Figure 4(b). If, as in
Figure 4{b), the node vector ~ is defined such
that n. is the value of the node indicated by (the
signifitant part of) the index vector Ij, then the
matrix obtained by appending!!. to l-provides an
unambiguous representation of the tree T. It is
convenient to also append the degree vector d
such that d. is the degree of (i. e., the numb-;;r of
-J
.
branches emanating from) node .!J. The resulting
matrix of v (T) + 2 columns is called a full list
matrix of T.

Any matrix obtained by interchanging rows
of a full list matrix is also a full list matrix and
is again an unequivocal representation of the tree.
If, as in Figure 4(c), the index vectors are right
justified and arranged in increasing order on
their value as integers (in a positional number
system), the resulting list matrix is called a full
right list matrix and is denoted by JT. If, as
in Figure 4(b~ the index vectors are left justified
and arranged in increasing order as fractions,
the list matrix is called a full left list matrix
and is denoted by CT.

(a,

FIGURE 3

(b)

(a)

b;)

PROGRAMMING AND CODING

350

The right list groups node s by leve Is, and
the left list by subtrees. Moreover, in both
cases the degree and node vector together (that
is, ~ 2/( 1T) or ~ 2/( (T)} can be shown to pro,ride an unequivocal representation of the tree
without the index matrix. If, as in the case of a
tree representing a compound statement involving operators of known degree, the degree
vector d is a known function of the node vector
!:" then the tree may be represented by the node
vector n alone. In the case of the left list, this
leads to-the familiar Lukasiewicz~:~ notation for
compound statements.

representation of the tree is therefore most
suitable. The analysis of a compound statement
proceeds by subtrees and the left list (i. e. ,
Lukasiewicz) form is therefore appropriate. The
index 'lectors of the lea,Tes of any tree clearly
form a legitimate Huffman prefix code and the
construction of such a code proceeds by combining subtrees in a manner dictated by the £requencies of the characters to be encoded, and
therefore employs a left list. However, the
characters are finally assigned in order of
decreasing frequency to the leaves in right list
order, and the index matrix produced must
the refore be brought to right list orde r.

App lications of Tree Notation

The tree notation and the right and left list
matrices are useful in many areas~~~:~. These include sorting algorithms such as the repeated
selection sort 4 , the analysis of compound statements and their transformation to optimal form
as required in a compiler, and the construction
of an optimal variable-length code of the
Huffman 5 prefix type. The sorting algorithm
proceeds leve 1 by leve 1 and the right list
2
3
First introduced by J. Lukasiewicz , and first analyzed by Burks et a1 .
_,.", For detailed treatments of the applications mentioned, see Reference 1.

r---------,
111
I
I

I
I

I
I
I
L ________ ..J

....d -n

,
I

(b)

(c)

T
(a)

FIGURE

351

A PROGRAMMING LANGUAGE

REFERENCES

Iverson, K. E., lIA Programming Language", Wiley, 1962.

Lukasiewicz, Jan, Aristotle's Syllogistic From the Standpoint of
Modern Formal Logic, Clarendon Press, Oxford, 1951,
p. 78

Burks, A. W.! D. W. Warren: and J. B. Wright: An Analysis
of a Logical Machine Using Parenthesis-free Notation lt ,
Mathematical Tables and Other Aids to Computation,
Vol. VIII (1954), pp 53 - 57

Friend, E. H., lISorting on Electronic Computer Systems It,
J. Assoc. Compo Mach. 3, pp 134 - 168 (March 1956)

Huffman, D. A., itA Method for the Construction of Minimum
Redundancy Codes", Proc. IRE, Vol. 40 (1952)
pp 1 098 - 11 01

353

DESIGN OF A ONE-MEGACYCLE ITERATION RATE DDA
R. E. Bradley and J. F. Genna
Hazeltine Technical Development Center, Inc.
Indianapolis, Indiana

Summary
This paper describes the design of
a parallel digital differential analyzer which operates at a rate of one
million iterations per second. SPEDAC
(Solid-State Parallel Expandable Differential Analyzer Computer) features
parallel organization of the integrators, serial-parallel arithmetic within
the integration cycle, 26-bit word
length, and the integral inclusion of a
digital function generator. The computer is progr~~ed in analog computer
fashion by means of plugboard interconnection of the integrators.
To achieve the one megacycle
iteration rate, the arithmetic circuits
operate at a six megacycle clock rate
performing trapezoidal integration.
The use of a parallel magnetic core
memory permits direct parallel communication and hybrid operation with external large scale general purpose digital
computers.
History
The first scientifically useful
differential analyzer computer was
designed by V. Bush and A. Ho Caldwell. l
It was an electro-mechanical computer
using 18 ball and disk integrators,
decimal constant multiplier gear boxes,
and servo-controlled relay switching
for interconnecting the integrators. It
provided a maximum of .01% accuracy in
the solution of differential equations,
and was used extensively by scientists
on a computing service basis during
World War II.
DUring World War LL ~ne development
of the voltage operational amplifier
allowed the construction of an amplifier
with extremely high gain and input impedance and near zero output impedance.
This made possible the construction of
an accurate electronic analog computer
in 19470 2 Since then the general purpose electronic analog computer has been
refined to such an extent that it provides easily set up, precise, accurate
(maximum of 001%), real time solutions
to elaborate mathematical problems requiring hundreds of operational

amplifiers. It also is used in simUlation stUdies to simulate portions of
physical systems. Within its area of
application, its economy is unmatched
by other types of computerso
The desire fo~ greater accuracy,
more flexibility, and simpler equipment
caused Northrup Aircraft, Inc. in 1950
to design the first digital differential
analyzer (DDA), designated MADDIDA.3 It
was an all binary, magnetic drum type
machine using rectangular incremental
integration and serial operation. In
comparison with analog computers, the
digital computation permitted greater
accuracy, the programming procedure was
more difficult, and the speed of operation was much slower.
A number of drum type, serial
memory, serial operation DDA's were designed in the next few years.4,5 These
included the CRC-I05, the Bendix D-12,
the Bendix DA-l, the Litton 20, and
several other special purpose computers
such as the Autonetics' VERDAN. Various
features such as decimal data entry,
trapezoidal integration, and solid state
circuitry were offered by various
computers. However, they all shared the
one common drawback to real time operation of being slow in operating speed
due to serial operationo
The first great leap forward in
operating speed was taken by Packard
Bell Corporation in the design of
TRICE.6 It is a DDA using parallel organization of the integrators (all required integrators coexist physically)
and serial arithmetic within the
integrators o Since all integrators
operate simultaneously, one iteration
cycle (in this case ten microseconds) is
just the time required for one integrator
to complete its updating process. Since
it is three orders of magnitude faster
than previous DDA's, it is capable of
performing real time computation for
many types of problems. The parallel
organization of integrators permits the
simplified programming technique of
analog computers through the interconnection of integrators on an analog

DDA AND HYBRID COMPUTATION

354

computer type patchboard.
The Hazeltine high speed DDA
designated SPEDAC (Solid-state Parallel,
Expandable, Differential Analyzer Computer) provides a further increase in
speed of one order of magnitude with its
one megacycle iteration rate, while retaining simple analog patchboard
programming. This increase in speed is
achieved by means of serial-parallel
arithmetic computation within the integrators in addition to the parallel
organization of the integrators. An
additional feature of interest to analog
simulation laboratory personnel is the
inclusion of a digital f~~ction generator as an integral part of its designo
Its design concepts are described in the
following paragraphs o
Design Concepts
General
The principal concept of the design
philosophy of SPEDAC is the realization
of a very high speed digital machine
which is operationally analagous to a
general purpose analog computer with the
increased accuracy and reliability of a
digital computer. SPEDAC is an all
solid state digital differential analyzer which is parallel in logical organization and serial-parallel in arithmetic
operation.
The system concept will now be
described with reference to the simplified block diagram given in Figure 1.
The inputs and outputs of every
computing element are wired to a plugboard. The computer is programmed by
patching the plugboard to interconnect
the computing elements in the desired
manner. The plugboard assembly is
centrally located in the rack assembly
in order to minimize and equalize the
signal transmission time between computing elements. The maximum allowable
transmission time between computing
elements is 40 nanoseconds (e.g. 40
feet of high propogation coefficient
coaxial cable).
Since the digital integrators
require six operational timing pulses
per iteration period, the one megacycle
model computer contains a master timer
which generates the six megacycle clock
pulses and distributes them throughout
the computer.

The master timer, illustrated in
Figure 2, consists primarily of a multiply tapped delay line and sufficient
gating to control the recirculating
start pulse. Since only six pulses are
required to synchronize the operation in
one iteration cycle, a start pulse generated either by the start button or
from an external control is gated down
the multiply tapped 1 ~sec delay line.
For a one microsecond iteration period
the start pulse emerging from the end
of the delay line is recirculated back
down the delay line with no external
delay. However, the whole system may be
time scaled downward by inhibiting the
output gates a number of 1 ~sec periods.
The length of this inhibit may be preselected by a binary counter and a
matrix enabled from a set of scaling
switches. Thus the iteration rate may
be scaled downward from one megacycle-by
any integral valus. Occasionally a
problem will arise where the programming
and scaling is greatly simplified if an
iteration rate equal to a binary multiple is available. For this reason an
additional .907 ~sec delay line is provided and may be switched in series with
the recirculating start pulse. This results in a basic period of 1.907 ~sec
and yields an iteration rate equal to
524,288 cycles per second or 2I9. This
rate may then be scaled down with the
counter and matrix to yield submultiple
binary iteration rateso
Computer Inputs
Data Entry. Data may be entered
into the computer either manually or
automatically. The manual input is by
means of a high speed keyboard, and the
automatic input is via paper tape, magnetic tape, Flexowriter, or directly
from a di~ital computer. This information is decoded into a standard 4-bit
binary coded decimal form and shifted
into the Message and Address registerso
The Address Selection Matrix receives
the address data and advances the memory
counters to the indicated memory address.
The Message Register presents the encoded
data to the Decimal/Binary Converter.
This converter sequentially translates
the binary coded decimal digits to pure
binary numbers and simultaneously adds
the binary numbers to obtain a pure
binary number equal to the multi-digit
binary coded decimal number in the
Message Register. This binary nwuber is
also present at this time in the Memory
Register and is loaded as the initial

355

DESIGN OF A ONE-MEGACYCLE ITERATION RATE DDA

condition into the register of the
integrator determined by the Address
Selection Matrix. The procedure is continued until all the initial conditions,
scaling factors, and integration limits
have been entered into the designated
registerso Since the information is recirculated back into memory as it is
read out, all of the input parameters
are retained in memory primarily for use
in a repetitive type of operational mode o
Additional planes of memory are utilized
as the Function Generator Storage.
Discrete breakpoints and associated
slope values of a function may be stored
in these planes by the operator through
the various means of input or directly
by a general purpose digital computer.
Computer Outputs
Data Readouto Data may be read out
of the computer in a continuous fashion
during a compute mode, or in a manual or
automatic fashion during a read out mode.
The continuous read out is accomplished
by interconnecting on the pre-patch
panel one or more digital-to-analog
converters. The contents of the Rand
Y registers and the initi~ conditions
stored in memory are read out in much
the same fashion as the data is read ino
Read out selection is accomplished
either through the external enabling of
the Address Selection Matrix, (manually
or automatically) or by sequentially advancing through the memory addresses o
The data is then presented to the Output
Register where it is stored during the
binary-to-binary coded decimal-todecimal conversion process o
Computing Modules
Digital Integrator. The high speed
of computation is accomplished by performing the arithmetic operations in
serial-parallel, that is, each register
is broken up into small sections which
add in an independent serial fashion,
and each section's carry is sensed
simultaneously in parallel. Thus, the
speed of operation (i.e o the iteration
rate) for practical purposes is independent of-the word length and the complexity of the carry gates is directly
proportional to the word length rather
than factorially as in an all-parallel
arithmetic o
The Integrator illustrated in
Figure 3 consists primarily of two of
these binary registers. One is called
the R Register and the other is the Y
Register. The initial conditions are

read into the Y Register in parallel
fashion from the initial condition
register in the memory unit. Signals
representing increments of one or two
dependent variables and their associated
signs may be plugged into each integrator via the pre-patch panel. In the
"compute" mode, the Integrator adds
these inputs to the contents of the Y
Register and adds one-half of this increment to the contents of the R
Register for the purpose of trapezoidal
correction. When an increment of the
independent variable is received, the
Integrator adds the Y register contents
to the R Register contents; thus, the
R Register contains

[n-j) Yo+ 1;..) ~~-I+ i 6 Ytl}~)(

which is the continuous integral of the
dependent variable function provided
the independent variable increment approaches a relative zero and the iteration rate approaches a practical
infinity. As the R Register fills and
overflows, the overflow is detected and
produces a signal which approximates
the equation

dz= (YI+Yz)clx
If the dz's are accumulated in a second
Y Register, the second Y Register will
contain an approximation to the total
integral,

z.::

fiy, + Yz')dx

The inputs and outputs of the integrator
are:
Inputs -

Outputs -

(1)
(2)
(3)

Dyl, Dy2
± sign dyl, ± sign dy2
dx

(4)

± sign

(1)
( 2)

± sign dz

During a typical iteration cycle,
the following operations are performed:
(1) Load the SQm of dylj dy2 into
the Y Register; and at the same time,
feed a trapezoidal correction to the R
Registero

(2) If a dx is present, add or
subtract the contents of the Y Register
to or from the R Register according to
the sign of dxo

(3) Determine if an overflow of
the R Register has been produced and

DDA AND HYBRID COMPUTATION

356

present on output dz.
The basic building block of the
Integrator is the counter-gate combination shown in Figure 4.
Counters #1 and #2 both contain N
flip flop stages. These counters count
up or down depending upon the condition
of the input ± line. Bits can be loaded
into any of the N stages of either
counter.
The carry storage logic receives
three inputs. These inputs are: (1)
Overflow from last stage of the counter,
(2) Counter Full enable from the
counter, (3) Carry enable from an external source o The carry storage logic
will present an output to the output
gate when input 1 £! when input 2 and 3
are presento
N connecting gates connect the outputs of counter #1 to the inputs of the
corresponding stages of counter #2. To
add or subtract the contents of counter
#1 to or from counter #2, these gates
are strobed by sequential timing pulses.
The number of timing pulses required to
combine the contents of counters #1 and
#2 and detect an output is N for the
connecting gates plus 1 for the carry
(N+l) plus 1 for the output gate, a
total of (N+2)o
The output gate is strobed by a
timing pulse after the above arithmetic
operation has been completed o
In the Integrators these basic
counter-gate blocks are combined into a
series network as shown in Figure 5.
The #1 counters now form a counter
register of NxZ stages. The #2 counters
form an identical registero
To add or subtract in register #1,
the bit is gated into the proper stage,
as determined by a scaling matrix, and
then the output gates of the counters
are simultaneously strobed to complete
the operationo
To add or subtract the contents of
register #1 to or from #2, each basic
counter-gate block described in Figure 4
simultaneously goes through the process
of gating #1 counter into #2 countero
Each output gate of register #2 is then
simultaneously strobed to complete the
operationo The number of timing pulses
used to complete this operation is still
(N+2) regardless of the number of basic
blocks used in the registers o

This method of implementing an
integrator by the use of counters has
the desirable characteristics of:
(a) The complexity of each basic
counter stage is independent of the
register size.
(b) The time required for the
addition or subtraction operation is
independent of the register size for all
practical register size requirementso
This enables the utilization of 6 megacycle circuits as opposed to 30 megacycle
circuits required in a 26-bit serial
in te gr a tor
0

(c) Fewer parts are used to
accomplish these operations than would
be needed for the conventional parallel
adder approacho
Block 1 of Figure 6 is the dy
summer and timer. The summer sums the
scaled values of dyl and dy2, then
strobes this sum into the Y and R
Registers. This sum is fed to the R
Register such that the rectangular increments of integration are corrected
to the more exact trapezoidal increments.
(The correction is accomplished by feeding +1/2 dy to the R Register as dy is
loaded into the Y Register.) Although
an inspection of the trapezoidal correction factor, with respect to an individual integrator, results in an
apparent error in the order of dydx, this
is not the case. Since the source of
the incremental input is a preceding
computing element, the information is
delayed one iteration period and would
result in a second order truncation
error if a -1/2 dy trapezoidal correction factor were used.
As these bits are bein~ strobed in,
the sign of the bit is fed to the Y
Register ± enable and to the R Register
± logic, Block 2. This sign information
thus determines the direction of count
of the two registers.
The loading of dy bits to the Y
Register may cause the register to pass
through zero or to overflow its capacity.
The overflow logic of Block 4 determines
either of these conditions by examining
the final carry storage logic of the
last stage in the Y Register, the sign
of the Y Register, and the sign of dyo
Should the Y Register pass through
zero, the overflow logic changes the
sign of the Y Register. Should the
cape.ci ty of the Y Register be exceeded,

DESIGN OF A ONE-MEGACYCLE ITERATION RATE DDA

357

then an alarm signal is initiated to
stop the problem.

registers, the C or Y register and the
IO (initial condition) registero

If the trapezoidal correction
causes the R Register to pass through
zero or exceed the capacity of the
register, then R overflow logic, Block 5,
will change the sign of R in the case of
passing through zero, or store the excess bit in the case of exceeding the
register capacityo

During operation, the constant
multiplier accepts one input, dX, and
produces an incremental output, CdX, in
which C is a constant. The· IO register
is used to enter the constant C into the
C register at the start of the problem.
In repetitive computations, the IO
register, which is located in the memory,
may be used to enter new values of the
constant C into the C register.

The next operation in the cycle is
the loading of the Y Register into the
R Register. This is triggered by the
presence of a dxo
Dx is fed into the dx storage and
timing logic, Block 3. This logic then
strobes (in sequence) the gates connecting the output of the Y Register to
the inputs of the R Register. This
logic is timed and controlled by the
synchronizer and the limits of integration set on this integratoro
During this portion of the cycle,
the ± enable for the R Register is controlled by the sign of dx through the R
Regis ter ± logic, Block 2.

When operating with a function
generator, successive values of C represent the successive values of the
function slopes as the function passes
from one breakpoint to successive breakpoints. The output of the constant
multiplier then represents an incremental rate, proportional to the slope of
the function.
Variable Multiplier. The products
of differential variables are formed
using the mathematical expression for
the differential of the product of X and
Y.
d(XY) = YdX + XdY + dXdY

The R overflow logic now determines
if an output has been generated by the
operations of this cycle, or if a sign
change is necessary for the R Registero
This decision is based upon the conditions of the last carry logic stage in
the R Register, the sign of the R
Register, the sign of the Y Register,
the sign of dx, and the results of the
trapezoidal correction. This completes
the cycle o
The Y and R Registers have read-out
gates which allow the contents of the
registers to be read out of the integrator. The Y Registers have read-in gates
which allow initial conditions to be
loaded into the registers. These readin and read-out gates are used in setting up the problem in the integrator
and examining the results of computations o
Constant Multi¥lier. The constant
multipliers are sim lar to the digital
integrator. In the constant multiplier
the Y register need not be a counter as
there are no dY inputs, and also the
trapezoidal correction logic is not
necessary.
The constant multiplier utilizes
one parallel accumulator register (the
R register) and two parallel static

This product is formed in the
SPEDAC variable multiplier with two
special integrators and a summing net=
work connected as shown in Figure 7.
The integr8.tors in the variable
multipliers differ from the standard
SPEDAC integrators in several ways.
Since a dY increment to the variable
multiplier is used as the dependent
variable increment for integrator #1 and
as the independent variable increment
for integrator #2, the timing of the
utilization of the dY increment must be
correspondingly synchronized. Therefore
the timing of the operational procedure
of integrator #1 is the same as that of
the standard SPEDAC integrator and the
timing of integrator #2 is inverted o
For rectangular integrators this
results in an output of the form~
Y(n-l)

Xn + X(n-l)

Yn +

This represents the exact differential product of the two variables X
and Y. Thus, the use of a variable
multiplier to accomplish variable multiplication is more desirable than the use
of two trapezoidal integrators, because
integrator truncation error is avoided.

DDA AND HYBRID COMPUTATION

358

Other Computing Elements. Several
other minor computing elements are available in the computer system, described
briefly as follows:
1. Digital Servo - One of these
minor elements is the digital servo
which is used as a decision gate or a
nulling device.
2. Summer - The summer accepts
the outputs and associated signs of any
other six computing elements patched
into its input and presents a binary
output plus sign equal to the algebraic
sum of the inputs which may be patched
into a following computing element.

30 Integration Limits - An
Integration Limit module is available
which is merely a counter and gating to
accept an incremental variable input and
either gate out or inhibit this increment depending upon a binary number
initially read into the counter. These
inputs and outputs are also patchableo
Function Generator
An unique feature of this computer
is the inclusion of a digital function
generator as an integral part of the
system. A simplified block diagram of
this component is illustrated in Figure

8.
A portion of the rapid access
memory is used to store twenty-two bit
words (21 bits plus sign), representing
the breakpoints and associated slopes
of desired functions. Data may be
entered into the function generator
storage via the DDA's automatic input.
The first three characters of a
function generator message contain an
address for one of the function
generators. The remaining characters
of the message specify the breakpoint
and the slope o The breakpoints and
slopes follow alternately in the sequence of breakpoint occurrence with
respect to the independent variable
increments c
After all the data have been read
into the memory unit and a "start compute" signal is received, the independent variable increments are gated into
their respective dX counters, and the
instantaneous value of each counter is
compared with the value in the breakpoint register. When the counter and
the breakpoint register contain the
same value, a compare signal assigns a

read-out sequence for use by the read
out control unit.
The read out control unit generates
signals to update the address register
and to enable the address gates for advancing the memory to the adjacent
location which contains the corresponding slope value. The read out control
also provides an enable for the Y
register gates to allow the slope value
to be read in parallel fashion into the
selected constant multiplier.
An independent variable counter and
a breakpoint comparator are used for
each f1L~cticn to determine the occurrence of the function breakpoints. When
a new breakpoint is reached, the new
slope is read (in parallel) out of
memory and into the C register of a constant multiplier. Between breakpoints
the same slope is retained in the C
register. The constant multiplier uses
the independent variable of the function
as its incremental input, and has an output whose rate is proportional to the
slope in the C register.
The function may be generated
either forward or backward with direction reversals accomplished within five
microseconds. The maximum reversal
rate is one per ten microseconds. If
more than one comparator senses a compare in the same cycle, each of the
indicated slope values is loaded into
its corresponding constant multiplier
before any of the breakpoint registers
are updated o In the event of a "worst
case" condition of five simultaneous
compares, all five slope values are updated in twenty microseconds. In this
case, another twenty microseconds is
required to update all five breakpoint
registers; a.nd a mlnlmu!ll spaclng of only
forty microseconds between the breakpoints of anyone function is required o
The number of breakpoints and
slopes per function is variable in
multiples of 32. As the number of
breakpoints per function is increased,
however, the number of f~~ctions capable
of being stored in the s ts.ndard memory
decreaseso For example, twelve 32
breakpoint functions, six 64 breakpoint
functions, etc., may be utilized o
Circuits
The high computational speed of
SPEDAC is due primarily to its parallel organization and series-parallel
arithmetic
Since only six pulse times
per iteration cycle are required, the
0

359

DESIGN OF A ONE-MEGACYCLE ITERATION RATE DDA

logical devices are operating well within the state of the art at six megacycles. Thus, conventional transistor
flip flops and cascaded diode gates
rather than unreliable or exotic electronic configurations are employed.
Furthermore, the series-parallel logic
provides a relatively easy transition
to higher computational rates as the
state of the art of semiconductors improves. Investigation of this expansion
is under constant evaluationo
Packaging
All components are mounted on 4" x
9" printed circuit cards which are assembled in removable drawers. These
drawers are in turn mounted on sliding
tracks in the cabinet assembly in a
manner such that the drawer is supported
by the track even when fully extended.
The majority of the one megacycle
enables throughout the system are
carried via teflon hook-up wire which
is loosely distributed in plastiC wiring
troughs in order to eliminate the cross
talk of a tight harness. The six megacycle clock pulses and signals are distributed via teflon coaxial cable
terminated with buffer amplifierso
The mid-section of the cabinet includes the writing desk, the control
panel and the patch bay. When seated at
the desk, the operator may easily reach
the control panel and the patch bay.
Four access doors at the rear of the
console provide access to the cabling,
power supply units and patch panel o
Applications
Quite often, when solving sets of
differential equations on an analog
computer, there exists an extreme contrast in the dynamic ranges of two or
more of the physical variables contained
in the equationso When the problem is
scaled such that the va.riables of major
interest lie within the dynamic range of
the computer, the accuracy of the remainin2 variables mav bA dAa~~dAd hAvnnrl
useful limi ts. In ~a~y~~~~~; thl;--;esults in very unrealistic values of the
points of secondary interesto
Due to the very high speed and
large range of SPEDAC, mating this computer and an analog computer in hybrid
operation will resolve many of these
difficulties by proper apportionment of
the equation variables. It is evident
that this computer is quite useful in

solving sets of equations requiring
differential computation with respect
to variables which are arbitrary
functions of time, partial differential
equations, and extreme dynamic range
problems such as missile and satellite
tracking problems requiring a uniform
degree of accuracy over the entire range
of values of the variables.
SPEDAC provides a very high speed
complementary computing aid for generalpurpose digital computers. The master
timer is so designed to enable complete
enslavement externally. Thus the inputoutput and computing modes of operation
may be in complete sypchronization with
rund under the complete control of a
stored program on a general-purpose
digital computer. The input-output data
are channeled through the High Speed
Data Transfer Register to and from the
fully addressable magnetic core memory
at data transfer rates up to 200,000
words per second. The data transfer
rate is limited only by the input-output
data transfer capability of the generalpurpose digital computer.
General-purpose digital computers
are relatively slow in solving sets of
simultaneous differential equations because the solution is performed by means
of numerical approximation methods using
iterative procedures. Equations involving many trigonometric functions also
reduce the computing speed of a generalpurpose digital comput~r, due to the
necessity of approximating trigonometric
functions by expansions in power series
or by means of table lookupso
SPEDAC is ideally suited to performing both of the above types of
computations at very high speeds, but
with digital computer accuracyo Thus,
its use in conjunction with a generalpurpose digital computer increases the
computing speed of the general-purpose
digital computer and consequently increases the work load potential of the
computing facllityo
References

Bush, V., and A. H. Caldwell: II A
New Type of Differential Analyzer",
J. Franklin Inst., Vol. 240, No.4,
pp. 255-326, Oct. 19450

Jackson, A. S., "Analog ComDutation", McGraw-ITill, pp. 3-5: 19600
Anon., "Computing Hachines",
Mechanical Engineering, V. 73, April
1951, pp. 325-327.

360

DDA AND HYBRID COMPUTATION

Donan, J. F., "The Serial Memory
Digital Differential Analyzer",
Mathematical Tables and Other Aids
to Computation, Vol. 6, No. 38
pp. 102-112, Apr. 19520

Mendelson, M. J., "The Decimal
Digital Differential Analyzer",
Aeronautical Engineering Review,
Vol. 13, pp. 42-54, Feb. 1954.

Mitchell, J. M. and S. Ruhman,
"The TRICE---A High Speed Incremental Computer", IRE National Convention Record, 1958. Part 40 (IRE
National Convention, New York, March
24-21, 1958)0

V6.U _ _ _
u6.v

VARIABLE
READ OU.T

READ IN

SUMMER

r-----

,r-I I

READ IN
READ-WRITE
ENABLE -----~

READ OUT

........-_~ r - -

r
I

I I r-------

~ -C>i

(

X2.~

Jxo

k6.x

READ-WRITE
ENABLE---~

DIGITAL/
_~ANALOG
ANALOG
OUTPUT
CONVERTER

READ IN

MEMORY
REGISTER

READ-WRITE ENABLE

-...-.......- - '

I
I

OR
GATES

I
I
6. z I

BINARY/
DECIMAL
CONVERTER

:....J

READ OUT

OTHER
INTEGRATORS
DECIMAL/
BINARY
CONVERTER

MEMORY

_-------1....

READ OUT
READ IN - - - - - - '
READ-wRITE
ENABLE

.-I

---

T3
T4
T5

MESSAGE AND
ADDRESS REGISTER

-. T2

MASTER
TIMER

AUTOMATIC
INPUT

MANUAL
INPUT

NOTE:

PERMANENT CONNECTION

MEMORY
ADDRESS

ADDRESS
SELECTiON

LIMITS
SERVO

PATCHED CONNECTION

OUTPUT

""---+-~-~

I I

CONSTANT

~ DIGITAL

--~
~

Figure 1. System Block Diagram

r---

AUTOMATIC
OUTPUT

HIGH-SPEED
DATA
TRANSFER

...-

DESIGN OF A ONE-MEGACYCLE ITERATION RATE DDA

r---To TI T2 T3 T4 TS

urnr

361

0.907 p.SEC
DELAY LINE

I
I

---1
I
I

.!.
I J.L SEC
DELAY
LINE

OUT PUT
GATES

START

•

.....--

CONTROL
AND
T.lMER

INH~BIT
I

COUNTER
AND
MATRIX

MODE
SELECTION

SCALING

Figure 2.

Master Timer

dx - .....----I~
d. Y --+----tl-__M' - -_ _
Y _ _tr

llY

II (XY)=Y n llX n +X n- I llYn
Yn II Xn = Yn-I II Xn + II X n II Yn
:.ll(XY) =Yn-lllX n +Xn-,llY n +llXn llYn

Figure 3. Digital Integrator

362

DDA AND HYBRID COMPUTATION
CARRY

ENABLE

±ENABLE

T~ M

1NG

OUTPUT
GATE

..___~

PULSE

TIMING
PULSE

CARRY ENABLE

±ENABLE

INPUT

Figure 4. SPEDAC Integrator Counter-Gate Block

I
I
I
I
I
I

INPUT
STAGE I

T(N+1l

I
I

IT
I

COUNTER

I
I
I

I
Figure 5.

INPUT
STAGE Z

SPEDAC Basic Integrator Registers

DESIGN OF A ONE-MEGACYCLE ITERATION RATE DDA

363

ADDRESS
SELECT

2
SIGN d X

[

CHANGE

LOGIC
~

SIGN

R
SIGN
SIGN

CARRY

OUT PUT
LOGIC

OUTPUT

dx
INTEGRATION..
LIMITS

TIMING
AND
STORAGE

GATES

ADDRESS
SELECT

•

I
SIGN dy I
SIGN dy2

dyl
dy2

......

---

SUMMER
AND
TIMING

CHANGE SIGN

::!:

SIGN dy

y
REGISTER

COUNTER
INPUT

CARRY
SIGN d y -----.
SIGN

ADDRESS
SELECT

OUTPUT
LOGIC

ALARM

y-----'

INITIAL
CONDITION

Figure 6. Integrator Logic Diagram

R REGISTER
SIGN Z
6x
GATES

SIGN

6Y,

6 Y

6Y2

Y REGISTER

INITIAL

CONDITIONS

n:k

n: 0

Figure 7. SPEDAC'S Variable Multiplication Method

364

DDA AND HYBRID COMPUTATION

I
AUTOMATIC
INPUT

BINARY CODED
DECIMAL TO
I
BINARY CONVERTER

ADDRESS
SELECTION

FUNCTION
GENERATOR
ADDRESS
REGISTERS

---..

CONSTANT ""'6 F (Xl
MULTIPLIER
>~-----....,.~

MEMORY

i
""'""-

Figure 8.

READOUT
CONTROL

Function Generator Block Diagram

INDEPENDENT
VARIABLE
AND
BREAKPOINT
COMPUTER

365

DDA ERROR ANALYSIS USING SAMPLED DATA TECHNIQUES
Don J. Nelson
University of Nebraska
Lincoln, Nebraska

Summary
Sampled data techniques were first
digital operations by Linvill and
Saltzer' in order to study the errors
resulting from the use of numerical integration techniques. The purpose of this
paper is to develop an understanding for the
mechanics of errors in the digital differential analyzer and to evolve a conceptually
simple error theory. This is accomplished by
establishing some of the basic comcepts
regarding the applications of sampled data
techniques to the integration process; developing the matrix model for the solution of a
system of linear differential equations with
constant coefficients on a digital differential analyzer and then using the W-transform
to finalize the error theory. It is then
easily shown that simple adjustments to the
coefficient matrix of linear differential
equations with constant coefficients will
allow one to obtain solutions to these equations the accuracy of which is limited only
by round-off errors.
appliedlt~

Mechanics of Error in the DDA
Fundamentals
Before progressing directly into the
analysis of DDA systems, it is desirable to
examine briefly some of the tools to be used.
The discrete nature of the variables in digital system~ allows the use of sampled data
techniques which are already widely used.
However, some of the concepts involved in DDA
systems are sufficiently different to warrant
special attention. Of particular interest is
the mechanics of integration.
If yet) is a continuous function, its
sampled counterpart can be represented by
y*(t) where
co

y*(t)

= yet)

•

Ln=l

S (t-nT)

It is to be noticed that given yet), y*(t) is
uniquely determined. However, the inverse
relation is not unique. That is, given
y*(t), there are an infinite number of
functions yet) that will yield the same
sampled function.

Quite frequently it is desirable to convert (by some practical technique) the samled function back into a continuous function.
If a Fourier analysis of the unsampledfsignal
shows that it contains frequencies f< 0/2
where f is the sampling frequency, the
unsampl~d function can theoretically be recovered identically by passing the sampled function through an ideal low-pass filter that
passes all frequencies below f . (This is
simply a paraphrase of the sam~ling theoremJ
As a matter of fact, in order to theoretically recover the original signal, the sampling frequency is required only to be at least
twice the bandwidth of the unsampled signal.
In the following work, recovery by practical techniques is not the point in question.
The concern here is with the sampled function
that has resulted and the sampled function
that is desired. This will be done by sampling the original continuous function, operating on this sampled function with approximate
operators and then comparing the result to
the sampled function derived from performing
the true operation on the original function
and then sampling this true function. Hence
the non-uniqueness of the derived sampled
function is not a matter of concern nor are
any of the previously mentioned recovery
restrictions.
The Laplace transform of the sampled
yet) is given by the convolution of yes) and
the Laplace transform of 6 (t-nT). This can
be written in two different ways:

lc yew) •

Y*(s)

_1_
2nj

Y*(s)

...L Ic
21tj

1
1 -

-wT

-(s - w)T • dw (2)

• yes - w) • dw

where residues are considered only at the
poles of the first function inside the
integral sign.
The two forms shown yield considerably
different appearing results. Equat\on (3)
yields residues at the poles of
T
1 - e-(I)
while (2) yields residues at the poles of
y«(I). Both equations shed some light on the
theory of sampled data systems.

366

DDA AND HYBRID COMPUTATION

Because of the prevalence of the function
e-sTin the esu~tions that follow, this work
will use z=e s as a sUbstitution where it will
simplify the equations. A¥other sUbstitution
that will be used is a=e-~. If these substitutions are used, the following transforms
may be obtained.

.'li.U

yes)

y*(s)

.£
s

__c_
1
z

( 4)

__
c_
s + Ot

__c_
1
e.z

( 5)

In general, then yes) will be of the
form

~
r=l

yes)

cta

Taz

(5 + a.) 2

(6)

- az)2

A.~,r

(11)

In order to understand the mechanics of
integration, consider a typical term from each
of the sums of (11).
First, let
A

-.2..1.!!
n
s

Then

(12)

Y*(5)

na _ _~c~__

+~~
i=l r=l

The reason for making the pole at zero a
special case is that integration creates a
special case for poles at the origin.

yes)
c

• d n-l (
dw n - l 1

(s + ~ )n+l

and
If concern is maintained for the solution
of linear or piece-wise linear systems, these
pairs are the only ones needed.

X*(s) - _1_
- 2n j

~(
w
n+l

=[~.
n!

Let yet) be a continuous function and
let
x(t)

(14)

(8)

yet) dt.

Second, let
Let yes)
yet) and
X·(s) be
stituted
parts.
Then
Y· (s)

X·(s)

and xes) be the Laplace transforms of
x(t), respectively, and Y·(s) and
the L~~Tace transforms (with z subfor e
) of their sampled counter-

yes) =

l,n

(s + a,)n

Then

----0

"c;

1"'1~

1
2'
I
nJ c

the convolution

integr~l~

Y*(s)
yew)

1
21t . I X(w)
J c

... ze

dw
wT ·
ze

1
1 -

1
1 - ze

1
_1_ I yew) •
wT
21tj c w
1 - ze

)

Jw= - a,

and
X*(s)

· dw

· dw.

\1
wT

Al,n
[ (n-l )!

(10)

Since sampling and summation are commutative, yet) can be broken into its exponential
components. This is most easily accomplished
in the Laplace transform domain by partial
fraction expansion.

•

d n-l (

dw n- l

A
--1..s.n

__1_

1 - z

w(l

WT»)]. w= - ~

DDA ERROR ANALYSIS USING SAMPLED DATA TECHNIQUES

Corresponding to the general term for
yes) in (11), the general terms for Y·(s) and
X"(s) are

Y·(s)

m [A
-L~
r=l

(r-l)!

k.J.

r-l

(.,.-1 ) !

-~.-

1 wT )]

l-ze

1
1-'7.'"

\ -

- -

w=o

II
I

.J w=

- (1

where quite amazingly f(t) is the unsampled
(continuous) function satisfying the sampling
theorem. This becomes an extremely powerful
and important relationship. Since f(t) is
continuous, it is possible to defferentiate
both sides with respect to t, getting

k.
J.

L L
i=l

r=l

...d..t£ • _1_

L L

i=l

(r-l)!

r=l

Note that

+ CnA

r-l ( ]
_d_
1
(19)
r l
wT
dw w(l-ze ) W=-(1

(w)B (w) ------ •
2

( 20)

One of the terms of (19) when expanded as in
(20) will yield

Y·,

J.,r

! l!!!
G(",),,,t/T dW
T
IV

d: [A(W)B(W)] yields
dw

2 n-2

_1_
2n j

fl(t)

l-z

(11

k.J. [ A

familiar with sampled data technique will
recognize that the expressions previously
derived are essentially in ZTtransform form.
(Ge¥erall y , however, Z is e S rather than
s
e- .) The W-transform can be defined by saying that if a function has a Z-transform equal
to F(Z), then the W-transform becomes
G(W) = WF(W). The inverse transform becomes

(18)

.L(_l
)w=o
L--2..L!:
wT
r=l r!
dw
l-ze

X·(s)

l (

L(
ti,,,

-.,.=1

i=l

dw -

r
L L --LL.
-_.
n

367

(s),

but the rest of the terms of the expansion
are not expressable in terms of Y·(s). This
is indicative of the difficulty of finding
some difference operator to operate on Y·(s)
to achieve, effectively, true integration.
In particular note that the Laplace integral
operator, lis, will definitely not be useable
as an operator upon the sampled function in
order to yield the sampled counterpart of the
integrated continuous function. This is
obvious anyway since lis operating on an
impulse function must yield a continuous function and not a sampled function.
The relatively involved computation indicated in (19) can be expressed mU qh more efficiently by use of the W-transform '5. Those

InW
Hence in the W-plane ~ becomes a differential operator--something which has not
been found for the function in the Z-plane.
The result of this discussion on integration
can be expressed diagramatically as in
Figure 1.
In the DDA, the purpose of the integrator
is to accept two inputs, ~x and ~y and to form
~z=y~x.
~ is then formed into z in the "y"
register of another integrator. In the connection of integrators, it is assumed that the
z formed is equal to the integral of ydx. It
is therefore necessary to examine the methods
used for this operation and then compare the
results with (19).
There are many methods of approx;m~ting
the integral of yet) based on samples' •
However, the primary two upon which operational DDA's have been based are rectangular
(Euler) integration and trapezoidal integration. These two methods will be compared with
(19). If any other techniques should be
implemented, the method of comparison would
be the same.
Rectangular Integration (Open Loop Integration)
In llclosed type:: rectangular integration,
the value of x at the time n is assumed to be

In a sampled data representation, ~t becomes
the sampling interval T, and (23) becomes

368

DDA AND HYBRID COMPUTATION
I

X*(s) - [x*(s)] .

[X*(s)] = zX*(s) + TY*(s)
I

[ X * ( s)]

Then, subtracting (25) from (19) yields

= _T_ • Y * ( s) •
(l-z)

U*(s)

However, an expansion of this last
function shows
x(O) + x(T)z + x(2T)z2 + ----

!ri.Q.L

=T [1 + z + z2 + --- ][y(O) + yeT) + y(2T) +

--1

(l-z)

i=l

r=l

k.J. [

A
i,r
(r-l)!

=Ty(O) + T [yeo) + yeT)] z

'1.') + yC 2T)
z2 +
+ T[Y( 0) + y\.,~'

which is in error from the desired equation
by an amount
Ty(O) + Ty(O)z + Ty(O)z 2 +
Hence the machine equation-must necessarily be

Trapezoidal Integration (Open Loop Integration)

• Y*(s) _ Ty(O)
[ x*(s)] = _T_
(l-z)
(l-z) .

(24)

The last term of (24) is essentially
taken care of in the machine by setting the
initial conditions. In the following work
yeo) will quite frequently be zero, thereby
eliminating the last term from consideration.
Establishing the general term for the
output of the machine integrator requires
having (24) operate on (18). This yields for
the rectangular integration case

~t--

Ao,r (' --1..- 0) _d__
r-l ('
[X*(S)] I= L
1
wT
r l
r=l (r-l)! l-z dw l-ze

')~"
w=O

-1'.;!iQl+
(l-z)

This function is fairly formida~le, but
leads to rather interesting results.
The
errors associated with the integration of some
rather simple functions are shown in Table 1.
It should be pointed out here, that the
process used in finding the error function
does not limit yet) to functions satisfying
the sampling theorem.

i=~
i=l r=l

n
In the interest of gompac~ness~Tlet dnjdw
be represented by D and iet e
be represented by Q. Also let the error function be

Trapezoidal integration follows the rule

[v [(n-l)Tl+
;

x(nT) = xL(n-l)Tj + Tl'

v(nT)l
W

J (28)

which becomes
I

[x*(s)] = X*(s)z + %[Y*(s)z + y*(s»)

or[x*(s»)'= y*(S)[T(l+z)l 2(l-z)j
2(l-z)

where the second term of (29) is required to
correct for the fact that yeO) may not be
zero.
Using the general term (18) for yes)
yields for the general case

369

DDA ERROR ANALYSIS USING SAMPLED DATA TECHNIQUES

Subtracting (30) from (19) yields the error
function

U*(s) =

~ Ao • r [(Dr_ 2rT(l+z)
(l-z)

Lr!
r=l

Ty(O)

2(1-z)

~ ~

~ ~
i=l r=l

Ai • r

(r-l)!

integration techniques.

nT
[If x( nT) =! y( t) dt,

open form integration techniques areOthose
that attempt to produce the true integral
from knowledge of x(mT) for m from zero to
n-l. Closed form integration techniques are
those that attempt to produce the true integral from knowledge of x(mT) for m from zero
to n.
However, the machine variable is discrete in nature. Since ~xi(nT) is added to
xi(nT) to produce xi(n+l)T , the next value
of xi is actually known and so it is possible
to 'Oroduce the "intell"ral increment" in closed
for~. Hence one ope;ation utilizes xi(nT)
to form ~i and then forms
X[(n+l)T] = X(nT) +

~X(nT).

Application of this formula to simple functions yields the errors shown in Table 1
under Trapezoidal Integration.

The formation of ~(nT) establishes the rule
of integration used by the machine.

Comments Regarding Open Loop Integration

Before continuing, consider the following
simple example. A system of equations

By straightforward, but rather lengthy
computations, it can be shown? that the maximum per unit error (magnitude) in the integration of a function with a pole at s=-o:
(regardless of the order of the pole) is
approximated by o:T/2 for rectangular and
0:2T2/2·3! for trapezoidal integration.
(Absolute errors are approximately T/2 and
T2/2·3! respectively.) It is interesting to
notice that there is no phase shift in the
integration of a cosine wave when trapezoidal
integration is used. This is a valuable
asset in closed loop DDA operation.

is represented on the machine by

Mechanization of the DDA
The digital differential analyzer is
sufficiently different, conceptually, in its
operation that, before proceeding, a few
words regarding its mechanization are in
order. The parallel type of operation will
be considered first.
Consider the set of simultaneous differential equations

= AX

+ F( t).

The machine representation is of the form

The schematic for the machine set-up is
shown in Figure 2.
The solution is initiated by establishing initial conditions for xi(O).
The xi(O)
are operated on to produce the ~Xi(O).
When the first ~t occurs, xi is updated to
produce x2(T)At which in turn forms the new
Ax 2 (T). This completes one full cycle. The
computer solution evolves as this cycle is
continuously repeated.
As previously mentioned, integration in
the DDA occurs in the formulation of the
function ~X(nT). The mechanized scheme may
use either open or closed form numerical
techniques.

Consider, for example, trape-

zoidal integration.
developed by
To mechanize this equation, the machine
utilizes xi(nT) to produce the values of
~X(nT), then uses both of these to produce
xi (n+l)T. At first glance, this would
seem to preclude the use of closed form

AX(nT)

= A[X(nT)

The quantity AXCnT) is

+ 6X;nT)]6t

+ ff(nT) ;

U(nT) ]6t.

DDA AND HYBRID COMPUTATION

370

This is the equivalent of the mathematical expression

(n+l)T
I
ydt 'B ~x(nT) ::: Y IiL(n+l);J +y(nT)
nT
L
-

= r(nT)

=~(nT)

:r(~T)

+ bz(nT) ]6t

6;y~nT)]

6t •

Hence
(n+l)T.

Xdt

nT
becomes
~n1a comp~1ca~ea Loe error theory somewhat but the analysis follows the same
pattern as that established in the following
work.

Analysis of DDA Techniques
This in turn becomes

In analyzing solutions to differential
equations on the DDA, it is desireable to use
the W-transform because one may use the differential operator in the W-plane.
If the W-transform is applied to the set
of equations

x
= 1 [

~t]-l
A2'

(34)

the result in the W-domain is
[ AX(nT)
ln w X(w)
T

+ (

= AX

F( nT) + F [( n+ 1 ) T] )}
2

f.t •

AX(w)

[lnT w I - A] X(w)
In the machine, ~t is represented by T,
so that the last equation can be put in the
form

x [2(1-Z)]
T(l+z)

= (AX +

F) •

Therefore, the machine's differential operator becomes

= o.

(36)

The determinant of the square matrix in

(36) yields a polynomial in (In w)/T which
when solved for yields the poles in the
W-plane.

2(1-z)
D*(z) = T(l+z)
•

For example, if sX-A yields a pole at
s= - ( I , then a root of the polynomial would be
(In w)/T = - ( I which yields a pole at w=e-a.T.
This is in accordance with the theory of
differential equations and W-transform theory.

In the serial type DDA, only one integrator is updated at one time. This means
that the mechanization takes on the following
form (for rectangular integration without a
driving function).

The problem, then, is what sort of error
occurs in the location of these poles if one
uses an approximate integration operator
rather than the true operator.

DDA ERROR ANALYSIS USING SAMPLED DATA TECHNIQUES

Substitution of the W-transform for the Z
form in (24) and (29) shows that the W-transform of the rectangular and trapezoidal
integration techniques are,
for rectangular:

[X(Wl{ = [,,:1] [Y(1Ol]' - T;:~'

for trapezoidal:

rvr_,,' _ rT(w+l)lrvr._,,1

Ty(O)
2(w-l) •

tMII'J - L2(w-l)JL Hw 'J

I~O\

\;;UJ

The differential operators, therefore,
are for the rectangular case :

371

An interesting observation may be made
regarding the solution of the equation
x" + ",2x = O. Here tch~ poles in the W-plane
should lie at w = ~JlO.
(Poles on the unit
circle yield undamped oscillations.) However,
if one uses rectangular integration, the
poles will lie at 1 + lOT (see Figure 3).
These poles lie outside the unit circle and
hence the solution will yield exponentially
increasing oscillations. The further they
are from the origin, the greater will be the
negative damping and the
the error in
the resulting frequency.
2. ~ Trapezoidal~.
of (40) into (34) yields

Substitution

(;~::ii)[X("'{ A
[X(Wl{ + ;:~'
=

for the trapezoidal case:

W-l)]rX(w)]'
[Y( w)]' =[2(
T(w+l} t

+ yeO)

(40)

w+l

The Rectangular Case.
of C39) into (34) yields

Substitution

(-;1 j[X(Wl]' = A~(wl]' - x(Ol
or

[(-;1) I - A]~("']' - x(ol
[X(wl{ =[(-;l)r Ar1X(O).

•

.::>

2: -

--~-

(43)

or for

22 • 3:
+ - - -

(4:-z3)(~T)4
23 • 4!
(44)

~iT.

a.T""

+---~-~-

w+l

(3!-22) (~T)3

I _ A]-l X(O)

This shows that the position of the pole will
be in error by an amount

Comparison with the expansion of e-~T
shows the error in the location of thelroots
to be
\~.T)-

[( T(w+l)
2(W':'1))

(41)

so that wi

and [X(w) ] =

(~~ ::i;)= -~.

If the true r~o~~ of the original equation
lie at wi = e ~~ , then the resulting polynomial in (w-l)/T will yield roots at
~
(WT-l)= -"",

[(~1::i;1 r - A] [X(wl]' = !~~'
In this case the poles occur for

The poles of rX(w)] are hence the roots of

the determl.naJi [( -;1) r

(42)

Therefore the product ~T must be kept small if
the solution is to closely resemble the true
solution. This requirement is similar to the
one discovered for small error in open loop
integration in the first part of this paper.

Again it is seen that trapezoidal integration
produces less error than rectangular integration. There appears to be an introduction
of a pole at w= -1, see (43). However, this
pole will be cancelled when the inverse of
the matrix is taken. This . i l l always be the
case regardless of the integration operator.
Hence the only frequencies present will be
the negative roots of the matrix (except for
those introduced by round-off errors).
considerin~ again the solution of the
equation x" + lO = 0, where the poles should
lie at w = e.:!:.jlOT, it is seen that the poles
lie instead at
1+jlOT/2
w =
1.:!:.jlOT/2 •

DDA AND HYBRID COMPUTATION

372

Since the magnitude of the numerator and
denominator are the same, the poles will lie
on the unit circle. Hence the solution will
be undamped and is at least without error in
this respect. The actual location of the
poles, however, is at
+ 2 tan- l wT/2
e.....

which means the location of the poles will be
in error by approxim~tely
+ . (wT)
e .- J """"'l2
This means the angle per unit error in W-plane
r"

(wT)

~""""'l2

(

The modified differential equation may then
be derived from
n

The resulting differential equation is
then put in matrix form and solved using the
desired operator. The matrix will generally
consistTof the constants of the type tangent
~ or e~. The accuracy is limited only by
truncation of these terms and round-off in the
computer. Hence, this technique could be
invaluable for accurate generation of simple
functions.

Comparison with Table L~ shows that

this is the same as the per unit error in the
magnitude of an integrated cos function.) For
an error of about 1 percent the product wT
should be about 0.33. This is rather interesting since it indicates that approximately
ten samples per cycle will yield 1 percent
accuracy in the resultant frequency. For an
error of 0.1 percent, thirty samples should
be taken; for 0.01, one hundred samples; etc.
In the closed loop system, establishment of
proper initial conditions will preclude any
error in magnitude since poles lie on the unit
circle. (This of course neglects errors
caused by rounding.)
It can be said, then, that theory regar~
ing sensitiv~ty7 and errors due to parameter
perturbation can be applied to DDA systems in
the W-plane. The perturbation of roots,
however, is more distinct since the differential operators are of a precise nature.

Rpund-Off Errors
Round-off errors are particularly difficult to resolve. Since these errors are
unpredictable without prior knowledge of the
solution, it would seem that deterministic
methods would fail to produce any useful
results. However, a few concepts are presented here which may be useful in some
considerations.
Consider the system of linear
differential equations

The ability to determine errors precisely
immediately suggests the possibility of modifying the original differential equation to
accurfl.tely produce the desired function--or
the desired solution to the original differential equation. This indeed is possible for
those functions that can be described by
linear differential equations with constant
coefficients. Here the rootssin the w-Plane
are given precisely by wi = e it, where the Bi
are the s-plane poles of the desired function.
If the poles of the modified differential
equation are Yi , then
for rectangular integration:
wi-1
eSi t_l
Yi=-T-=

Inm w Z( W,\

2(w.-1)
~

AX( w).

The machine equation is actually set up
to perform
[X(W»)

= O(w) [A][X(W)] -(W~l)AX(O)
+

~w: 1)

X(0)

2(e s i t -l)
T(esit+l) •

(45 )

where O(w) is the mechanized integration
operator, and the k is a constant necessary
to achieve the proper initial conditions,
mathematically. The roun~-off process Can be
considered as the addition of some function,
£(w) to the function after the "integration"
operation has been performed.
Equation (45) then becomes

[XCw)]

= O(W)A[X(W)] -(W~l)AX(O)

+(W:l)X(O) + E(w).

and for the trapezoidal integration:
Yi = T(w.+l)

AX.

In the W-transform domain, this becomes

Function Generation

(s-Y i )·

i=l

(46)

DDA ERROR ANALYSIS USING SAMPLED DATA TECHNIQUES

I
-1
So [X(W)] = [I-O(W)A] {l-kA] (W:l)XCO)

373

Hiller, K. S. and Murray, F. J., "A Mathematical Basis For An Error Analysis of
Differential Analyzers", MIT Journal of
Mathematics and Physics, Vol. 32,
-July-October 1953, pp 136-163.

Nelson, Don J., "A Foundation For the
Analysis of Analog Oriented Combined
Computer Systems", Ph.D. dissertation,
Stanford University, 1961.

+ E(w)l·

Supposedly the poles of E(w) will be
more or less randomly distributed in the
normal case. However, it is observed from
(47) that should poles Of~E(W)~COinCide with
poles of the "unrounded" X(w) , it would be
possible to obtain almost
y ind of error
from the round-off procedure. However, E(w)
cannot have poles of higher order than one by
nature of its origin. This means that the
worst effect that could occur would be to
increase the order of some "natural" pole by
one. The worst type of pole would be one
lying on the unit circle in the W-plane since
this would give a response of tsin ~t in the
equivalent uns~pled domain. If one should
know the location of the poles in the
"unrounded" [X(w)]', it would be possible to
set a bounds on the error by assuming the
worst case, namely one pole in E(w) lying on
each pole of [XCw)]I.
It is believed by the author to be not
possible to extend the theory of error caused
by round-off any further than has been done
in the previous discussion if deterministic
methods are to be used. However, it is
possible that some statistical studies might
show that this type of error has some predictable distribution.
References
1.

Linvill, W. K. and Salzer, J. H., "Analysis of Control Systems Involving Digital
Computers", Proc. IRE, Vol. 41, No.7,
July 1953, pp 901-906.

Salzer, J. M., "Frequency Analyses of
Digital Computers Operating in Real
Time", Proc. IRE, Vol. 42, No.2,
February 1954, pp 457-466.

Suskind, A. K., Editor, "Notes on AnalogDigital Conversion Techniques", John
Wiley and Sons, Inc., New York, 1957.

Gilliland, M. C., "The lI-Transform", a
paper presented at the Northwest Joint
Computer Conference, October 1960

Gilliland, M. C., "The Spectral Evaluation
of Iterative Differential Analyzer Integration Techniques", Proc. West. Joint
coSp. Conf., Vol. 18, May 19'6"1," pp 50751 •

Hildebrand, F. B., "Introduction to
Numerical Analysis", McGraw-Hill Book
Company, Inc., New York, 1956.

374

DDA AND HYBRID COMPUTATION

yet) --+ yes) - - /~ Y*(s)~ y*(z)

Jty(t)dt
0

!
x(t)

~
~

not 1s

not s1

~0----+- X*(s)~

Figure 1.

4.J

Integration Operations.

Figure 2.

tenw

Y*('7'\~

.. .a..

yeW)

v(,.,\
A\OJ

Machine Representation of X = AX.

Y(l,r
~
•• .I

~.,

DDA ERROR ANALYSIS USING SAMPLED DATA TECHNIQUES

375

poles from
rectangular
integration

desired poles

Figure 3.

yet)

Location of Poles

clx = O.

True Integral

Trapezoidal

_ Tt
2

2
T t

2
t
2:

-1+"-1'2

t3
3:

- 1'2 - 2'4"

t!+

4:
-o:t

Absolute Error (Equivalent Continuous Function)
Rectangular

-at

cos CQt

Tt3

T2 t 2

Tt4

2 3

1: te=g, t
2

1.
2

_ T2 t 2
12

T2 t.3

- """72 o:T

-12 (1

_2
"J."
e-0: t)
- 12 (1-

+ CQT sin CQt

3
t
3!

e-o:t )

- "2T

cos CQt

O:'J:

+ 12

CQT2

1'2

-e

-0: t

- 1.
2

T
2 sin CQT/2 sine CQt + CQT/2)

Table I.

T t
r:

5!
)

_1
0:

_2
te-o:t - -'.I.' (1- e-o:t)
12

- !0:

sin CQt

Actual Function Developed
cos CQt

-T

2
T t

T t
T t
-V-12-r:

- 1.2 (1 -

T cos CQTL2 sin CQt
2 sin tlJT/2

Absolute Errors.

.!CQ

(1 - e-0: t)

-0: t

..!..2 (1 - e-0: t)
at

sin CQt

377

HYBRID TECHNIQUES APPLIED TO OPTIl\tIIZATION PROBLEMS
Hans S. Witsenhausen
Electronic Associates, Inc.
Princeton, New Jersey

Summary
A function dependent on the solution of a
set of differential equations containing adjust~
able parameters, can be minimized by systematic
search procedures in parameter space. Such procedures can be implemented by a hybrid system
consisting of a general purpose analog computer
and a digital expansion providing parallel logic
building blocks. Programming of such a system is
illustrated for a simple search procedure in
n parameters.

The full possibilities are realized by speeding
up the usual real-time operation where the operator makes intelligent decisions between computations, on the basis of the fresh information just
obtained. Successive computations can then be
distinctly different.
The digital modules are interconnected on a
removable patch panel. Programming is conveniently similar in principle to the approach
familiar to analog computer users.
Digital Expansion System

Introduction
General Features
The solutions of many problems benefit from
the use of a combination of both analog and digital computing devices. The required hybrid
techniques of computation can be carried out by
the linkage of an analog computer with a general
purpose digital computer. For iterative solution
of problems, in particular system optimization,
a more desirable approach is the addition to the
analog computer of a digital expansion system designed to provide primarily:
(a) Flexible automatic logic control of an
analog computation or a long sequence of analog
computations
(b) Large capacity, fast-access storage for
problem solutions requiring a sequence of computations with variable function storage.

The digital expansion system building blocks
use two voltage levels to represent 0 and 1. A
connection carrying a 1 level is said to be energized. Logical functions can be mechanized by
interconnection of gates operating on these
levels. Sequential logic requires flip-flops.
Changes in the state of a flip-flop are clocked
by a central system clock. Frequency of the
clock pulses is adjustable from several megacycles down to manual control, pulse by pulse, by
a pushbutton. This enables the operator to check
parts of the set-up at leisure.
Counters provided with the system can be
used to generate signals at binary or decimal
submultiples of the central clock frequency.
Logic Building Blocks

The assembly of many analog and digital computing components in an integral system gives the
programmer complete flexibility in his organization of a problem solution. To demonstrate what
is possible with such a system this paper considers a problem solution which makes good use of
the flexible automatic logic provided by the proposed digital expansion system. For simplicity
in explanation, this more basic feature of the
hybrid computer is applied to the solution of a
straightforward problem in optimization.
The digital expansion system provides "logic
building blocks" which can be connected to form
in this case the automatic control of the optimization program. These digital modules are electronic (solid-state) devices providing high computing speed. Any logical function could be implemented by relays and stepping switches, as has
been done iO ~any analog computer applications in
the past. 6 ,1,oHowever, higher speeds, flexibility
and programming convenience are required in order
to take full advantage of the speed of analog computers. This is not done in the repetitive operation mode where successive computations are simply
repetitious or differ only by small perturbations.

For the present purpose, only four types of
building blocks are required: (See Fig. 1)
(a) AND gates (2 inputs), the negated output
is provided.
(b) OR gates (up to 6 inputs), the negated
output is provided. (AND and OR gates, although
logically interchangeable through negation, are
distinguished for ease of intuitive programming)
(c) General purpose flip-flops (GPFF)
These are clocked RST flip-flops. The
S (set) input commands the 1 state; the R (reset)
input the 0 state; the T (trigger) input commands
state reversal. Only one of these inputs may be
energized at a time. The input levels are sampled by the clock pulse. Changes in state take
place accordingly after disappearance of the
pulse and the new state is established before the
following pulse. Assembled in groups of four,
these flip-flops have two group-input controls:
a"clear" input which resets all four, and an
"enable" input which can be used to inhibit the

DDA AND HYBRID COMPUTATION

378

RST inputs.
(d) Quadruple flip-flops in shift register
connection. (QFF) These are sets of four flipflops with internal connection into a shift register. Each set has eight outputs, the 0 and 1
states of each flip-flop.

computer users. To this effect, it considers the
general optimization problem which is both significant and representative of the class of applications requiring logic operations rather than
large capacity storage.
For clarity, no attempt is made to reduce
the number of building blocks to a minimum.

The inputs are as follows:
Use of Subroutines
Serial Inputs: The serial set (SS) and serial
reset (SR) inputs are applied only to the first
flip-flop and can be patched, in particular, from
either the output of the last flip-flop of another
QFF package for construction of long registers or
the output of the last flip-flop in the register
for closure of a loop.
Shift Input (SH): Transfers the state of each
flip-flop to the next in order on one clock pulse
and enables the serial inputs to control the
first flip-flop.
Clear Input: (CLR) Resets all four flip-flops.
Set and Load Inputs: One set input(S) is provided for each flip-flop. The load input (L) is
common to the building block. When the load input is energized, flip-flops for which the set
input is energized will go into the 1 state.
Programming of the Digital Expansion System
The techniques for programming a digital expansion system are presently unfamiliar to most
analog and digital computer users. The program
is not introduced as a list of successive instructions but as a set of patching connections.
This implies a task of organization similar to
that needed in the design of a digital computer.
However, there is considerable difference in the
emphasis placed on component economy. Economy is
essential for a computer design but of little
concern in the programming of the digital expansion system as long as enough components are
available. Thus, an empirical approach to digital expansion system programming, by successive
simplifications and rearrangements is entirely
acceptable.

Operations in the analog computer have to
follow a definite time sequence. Whenever a sequence of operations has to be repeated many
times, it is defined as a subroutine. One way to
implement a subroutine is to use a ring counter,
acting effectively as an electronic stepping
switch, where the sequence of states determines
the sequence of operations. A ring counter is
obtained by assembling QFF units into a shift
register of the desired length and then connecting the outputs of the last stage to the serial
inputs of the first QFF. Initially the first
flip-flop in this loop is set to the 1 state and
the others are in the zero state. When the shift
input is energized each clock pulse will advance
the sequence by moving the I state to the next
flip-flop resetting the previous one. After all
flip-flops have been energized successively the
next shift returns the ring to the initial state.
Each flip-flop can command in parallel a set of
operations, including the initiation of other subroutines.
The effective use of subroutines depends on
two features:
(a) Appropriate control by other routines.
(b) Provision for delays necessary for
operation of analog components.
Control of Interlocking Subroutines
When a routine calls, at one stage, for the
execution of a subroutine it is often necessary
to halt the advance of this routine until the
subroutine has gone through its entire cycle.
This interlock can be obtained by the formation
for a given subroutine A of 3 signals.

The logic building blocks provide entirely
parallel operation though it is possible to perform digital operations serially when desired.
The digital and analog programs are introduced
by their respective patch panels and interconnected by trunk lines forming one single set
of parallel analog-digital components.

sA: this signal is the call for subroutine
A, it is formed by an OR gate which receives
signals from all the sources of calls, generally
different positions in one or more other routines.

Several signals from analog comparators can
be accepted simultaneously and combined to form
several logical functions, while simultaneously
several commands to analog switches (electronic
relays, analog memory, mode control) can be generated.

eA: this signal is generated at the time
routine A returns to its initial state. It is
produced by an AND gate supplied from the last
state of A and the shift input of A. The eA signal is energized for one clock time and is called
the end signal of subroutine A. If a subrouti.nE>
should be repeated n times, a separate counter
(analogous to index registers) can be used to
produce the end pulse.

This paper shmvs some aspects of this programming technique, for consideration by analog

HYBRID TECHNIQUES APPLIED TO OPTIMIZATION PROBLEMS

x
eA : this signal is produced by an OR gate
supplied by eA and by the negation SA of sA.
x
Called the interlock signal, eA is fanned out to
all routines which call subroutine A.
The required interlock is obtained by supplying the shift input of a routine by the AND combination of its own call signal and the interlock
signals of all the routines for which it calls.

Some routines control electronic relays, analog memory and mode of integrators in the analog
computer. When exercising such control the routine must incorporate delays to allow sufficient
time for changes in computation to take place so
that solutions do not include the transient
response of amplifiers and the charging of capacitors necessary between consecutive operations.

These delays can be obtained by an AND gate
at the shift input to the routine; this gate is
fed by the shift command and timing signals of
slow rate derived from the carries of the central
clock counter. Different rates can be used in
different routines.

379

of the applied digital level. In many cases, a
GPFF will buffer these commands so that the condition of the gate is maintained until new signals
are fed to the GPFF. One GPFF can control several gates in synchronism.
Signals From Analog To Digital Eguipment
Particular signals produced within the analog computer are transferred to the digital
equipment. These signals provide information of:
(a) The analog computer mode, and
(b) The state of comparators
The computer mode signals are ICL, HL, and
OPL which are energized whenever the analog computer is in the initial condition, hold, or
operate mode, respectively.
Comparators will supply one of two levels
depending on the sign of the algebraic sum of
their analog voltage inputs. These levels are
normalized for direct utilization in the digital
system.
The "Optimization Problem"

If delays of different sizes are required in
the same routine, the routine itself can switch
control from timing signals of one rate to those
of another. Alternatively general purpose delay
units (one-shot multi-vibrators) can be used to
inhibit shifting during the required time span.
The delay required while the analog computer
is going through an operate cycle, is obtained by
inhibiting shifts of the controlling subroutine
in the operate mode; this takes care of the cases
where the run time is variable, depending on some
condition in the problem.
Signals From Digital To Analog Eguipment
Signals computed by digital components and
transferred to the analog computer are required
for the following purposes:
(a) Control of the analog computer mode.
(b) Control of the mode of individual integrators or groups of integrators.
(c) Control of analog storage units.
(d) Control of electronic gates used for
switching operations.
For the control of the analog computer modes
(OPERATE, HOLD, INITIAL CONDITION) input terminations are provided on the digital patchboard. A
pulse applied to any input termination will trigger the corresponding mode.
The other control functions are effected by
electronic gates which accept digital signals.
The opening or closing of the gate is a function

A set of algebraic and differential equations, mechanized on the analog computer, uniquely determines in one computation (the run) a
value E, the loss-function or error-function to
be minimized by manipulation of n parameters
Al ••••• ,An'
This problem occurs in many situations;
--solution of a set of algebraic equations
--matching of boundary conditions
--search for eigenvalues
--process optimization
--model building
--curve fitting
etc ..•..•
While special techniques exist for each class of
problem, the general problem is considered here.
l
Analytical methods ,2,5 for solving optimization problems, such as that of steepest descen~
make use of partial derivatives determined either
from the analytical proble~ statement or by parameter influence techniques. The experimental
approach considered is quite different conceptually, for the search for an optimum is entirely
based on repeated tests with differ~n6 parameter
combinations. Experimental methods' can use a
varied degree of sophistication to accelerate
convergence to an optimum and to overcome possible difficulties due to the teatures of the unkno"tm hypersur face. E (AI'····· ,An) •
The price of refined search procedures increases very rapidly with the number n of parameters. For the purpose of illustrating the
methods of hybrid programming of any search tech-

DDA AND HYBRID COMPUTATION

380

nique the following simple approach is selected.

also defeat more elaborate and equipment-consuming
alternatives.

Search Procedure
Assurr.e normalization of all parameters so that
a unique !!exploration distance!!, h (say 1 volt on
a + 100 volt computer), is acceptable.
Given A. and E at an arbitrary starting
point, the !~rst pa~tial derivatives are approximated by

If a Euclidean metric b~sed on voltage is
used,
the step length 6~
will. vary _ between
.
.. r - . . .
. ~..
.
c::, and. c::,'.j n d.epend.~ng on the d.J.rection selected.
This is acceptable because there is no a priori
reason for a voltage metric to have special significance.
Program Refinements:
The procedure outlined above can be improved
at a small expense in equipment by addition of the
following features:

where
5E+i

E(Alo,···,Aio+h, ••• ,Ano) -Eo

5E- i

E(Alo,···,Aio-h, .•• ,Ano) -Eo

All n partial derivatives are thus approximated by means of 2n calculations of E (runs).
In order to place most of the load in the digital
part of the hybrid system, the values of the partial derivatives are stored in quantized form.
Instead of storing dE/dA., a quantity p., susceptible of only 3 value§, is defined b~ comparison \vith a limit L selected by the computer
operator. Extension to a higher number of values
poses no special problem.
Pi

-1

BE+

if -2hL
if

< -

BE+ - BE

BE+ - BE-

2hL

> 2hL

The vector with components p. defines a direction in n-space in which a de2rease in E is
probable. It is close to the steepest descent
direction for which the components are dE/dA .•
The program stops if all p. = O. Hith one 6f
the 3n -l possible directioRs determined, the
parameters are changed to A. + P'~l' where 6 1 is
a fixed quantity (say 2 volEg). ~II an improvement, indicated by a decrease in E, is obtained
the values of all parameters A. are "updated" to
give a new starting point. Ada~tional changes by
steps, 6 , in the same direction are carried out
1
until no more improvement occurs. Then a smaller
step-size 6 (say .2 volt) is selected and when
2
this also fails, the partial derivatives are redetermined and the process repeated. If, after
a new determination of the quantities p., even a
single small step leads to no improvemeRt, the
program stops. If the analog computer does not
overload,the program will ultimately reach one of
the stop conditions and this should occur in the
vicinity of the optimum.
An advantage of this technique is that the
equipment requirement, as demonstrated later, has
a slow linear increase with n. It is recognized
that many possible features of the E function
(high curvatures, local minima, narrow winding
"canyons", etc.) will defeat the search procedure;
on the other hand, the very same features can

(1) If: after determination of direction i at
least one large step 6 1 is successful, then no
small steps are used before a new determination of
direction. However, when a single large step does
not decrease E, a smaller step 6~ is used. This
program arrangement is a time~sa~ing feature.
(2) For non-convex E functions it is
necessary to redetermine direction from time to
time even if improvement is constantly obtained.
To this end an upper limit N (say 8) is put on the
number of steps in a direction before redetermination of direction.
(3) The limit L for quantization of the
slopes should be carefully chosen. If L is too
large, the program will stop in any "flat" region
of the E-function and for non-convex functions
this final value of E may be far from a minimum.
If L is too small, all quantities p. will have
values ±l most of the time. This h~s the disadvantage of reducing the effective set of possn
n
ible directions from 3 _l to 2 (for n=6 from 728
to 64) and therefore the efficiency of .the search
procedure.

Many refinements are possible to avoid this
difficulty. The following is selected for its
economy of equipment.
Each slope is compared with two limit values
Ll an~ ~2 (L l < L2 )· If no slope exceeds L2 the
quantJ.tJ.es p. are based on L . If any slopes exl
ceed L2 the &uantities P. are based on L. This
procedure is poor whenev~r many slopes a~e clustered in a narrow range around either L1 or L ,
2
but this is unlikely to happen frequently in a
long optimization. The procedure requires just
one more comparator in the analog computer.

(4) Whenever desired, half the exploration
runs can+be sa~ed by +eplacing the slope evaluation BE - BE by 5E ,that is use forward in2h
11"
stead of central differences.
Analog Program
From the statement of the optimization procedure the analog circuit (Fig.2) can be derived
immediately as follows.

HYBRID TECHNIQUES APPLIED TO OPTIMIZATION PROBLEMS

The problem equations are mechanized by circuits which accept n input signals ~i' The last
updated values of the parameters~. are held on
n analog memories. The size h, ~L;oor ~l of the
1ncrements 5~ is selected by Z s~V1tches and distributed with both signs to n pairs of switches;
for each parameter one switch determines the sign
of ~_ the other determines the addition of 5A.
to ~.1. This addition is performed by an ana16g
memof~ so that the new value ~. =~. + 5~. can
be transferred to the~. memofies ~gen upaating
of the parameters is re~8ired.
The duration of the operate period (the run)
is determined in general by the problem itself
and can be dependent on the parameters. A comparator produces the hold signal when the appropriate condition is satisfied. At that time the
value E becomes available.
The previous updated value E is held on a
memory amplifier. The differencg E+- E is_fed
to two memory amplifiers so that 5E ana BE can
be successively computed, stored and then compared. The value E itself is stored to permit updating of E when required. If the problem integrators canoconveniently be used as storage for
the value E the number of analog memories required at the output can be reduced from four to two.
For determina~ion o! the direction parameters
p. the sign of BE - BE is sensed by a comparat6r, and the absolute value of this difference is
compared with two constants by two more comparators.
After a step has been carried out the change
in the E functio~ is stored in one of the 5E
memories, say 5E , and the sign of this quantity
is sensed by a comparator to determine whether
improvement has been obtained. Table I shows the
conditions fo~ digital control of the circuit
switches.

381

The comparators deliver information about
the E-function to the digital equipment according
to Table Z.
Digital Expansion System Program
The digital expansion system program must insure that, once begun, the computation progresses'
automatically in its search for an optimum. This
part of the program has inputs only from the IMP,
N, L , LZ co~parator signals and the analog comI
puter moae s1gnals.
Program Structure
The first step in producing such a program
is to specify a flow diagram of the required sequence of operations. (Fig. 3) This flow diagram
organizes the operations into the following subroutines:
Master Routine: selects the step size h,
~
tests the two stop conditions and calls
alterna~elY for the subroutines Explore, for determination of a direction, and Proceed, for
carrying out steps in that direction.

Explore Routine: calls for a computation of
E with a single parameter displaced by +h then by
-h. It steps through all parameters storing the
p. as they are obtained. Hhen all p. have been
oBtained it sets the B~. switches acEordingly.
1

Run Routine: executes the computation of E
for the prevailing ~i values.
Proceed Routine: A step size (~l or ~ )
being selected by the Master routine and a ~irec
tion (a set of p.) having been set by the Explore
routine, the Pr02eed routine displaces the ~.
accordingly, calls for computation of E and Eests
for improvement. The routine repeats as long as
improvement is obtained, unless a preset number

TABLE 1
DIGITAL LEVEL

UNITS
0

Lll

BA.
. 1 Off/On relay
i = 1, 2, ••. n

Off

B~. + / - relay

!J. /b.

h/~

relay

store

track

Stores for -E and -~i

track

store

5E+ store

track

store

- store

track

store

Stores for E and
0

382

DDA AND HYBRID COMPUTATION

of steps is exceeded, and calls for the updating
routine after each improvement.
of

Update Routine: transfers the present values
and E into the ~io' Eo memory units.

Program Mechanization
The subroutines are instrumented in detail as
follows:
Subroutine C (Fig. 4) (RUN) will start with
the analog computer in its IC mode. The call signal sC is obtained by an OR gate (not shown)
which combines all sources of calls from the
EXPLORE and PROCEED routines. The routine will
be started after new commands have been given for
the 8~; a delay is necessary for acquisition of
the new ~i by the analog computer (especially if
some of tfiem are initial conditions). Next the
OF mode is triggered and the subroutine ir~ibited
by the OP level. Upon automatic hold, the routine resumes with a delay to allow for ac~uisi
tion of the final 8E values. Then the 6E store
and, if permitted by a signal ENHM (enable hold
minus) generated in the EXPLORE routine, the 8Estore are switched to hold by setting the flipflops controlling the memories. After another
delay, the subroutine returns to its initial
state, generating the end signal eC. The interx
lock signal eC is used to inhibit the calling
routines.
Subroutine D (Fig. 5) (UPDATE) will update
the ~io' Eo values to ~he last ~i' E values.
Here
delays are prov~ded to enable the tracking
stores to acquire steady-state values. Since
only two states are required the ring counter is
replaced by a GPFF with the trigger input acting
as the shift control. Signals eD and eDx are
x
generated, eD inhibits the PROCEED routine.

The delays for subroutines C and D are obtained by the use of a slow clock rate (SLCL) derived from a carry of a clock counter.
Subroutine A (Fig. 6) is the program for determination of approximate partial derivatives
(~XPLORE1.
It is associated with shift registers
8 , 8, W, N.
x
8 and ~ control the analog value of 8~:
The data obtained during exploration is stored in
registers 8 and N.
x
The subr~utine begins with the 8 , ~ cleared. First 8
is loaded and subroutine C called
then NIx is 1 loaded (implementing 8A=-h) and subroutine C called with ENHM turned on. At this
stage the correct value of N, L , L2 appear on
l
the comparators. A test is carried out to determine which comparison level should be used. The
first occurence of a slope> L2 will clear all
previous 8's, set flip-flop L, which controls determination of future 8's on the basis of L2
alone. If L2 is not exceeded, 8's are selected
according to L • The routine shifts the new data
I
into the 8, N stores, sends the 8E memories to
the tracking mode and repeats, shifting to the
next parameter.
When the last parameter is
x
reached the 8 , ~x are cleared and the 8, N are
transferred into 8 , ~ registers in a parallel
loading operation. The end signal and the interx
lock signal eA are generated.
Subroutine B (Fig. 7) will carry out steps
in the chosen direction (PROCEED). It calls
upon subroutine C for an analog run, then senses
the IMP comparator level. (l,f no-improvement is
obtained the end pulse eB
is generated. If
improvement is obtained, subroutine D is requested for updating and the S flip-flop associated
with the master routine is set, to record success.

TABLE 2
Digital
Level

Analog Condition
+
sgn BE
sgn (8E

8E+)

Name

Meaning

0
I

IMP

Improvement

Best direction
is 8>..1< 0

Change in
advisable

sgn

[I 6E - -8E+ I

·2hL.
J

0
1

HYBRID TECHNIQUES APPLIED TO OPTIMIZATION PROBLEMS

The end signal eD of the UPDATE routine increments a counter (r) and subroutine B re2eats unless r=N where the routine end pulse eBl2) is
generated. The two types of end signals xare combined to generate the interlock signal eB •
Master Routine M (Fig. 8) first calls upon A
for exploration, selecting step size h. Next it
tests the stop condition 8 = .• = 8 = O. It
then calls upon B (PROCEEDt with thenlarge stepsize ~l' If, and only if, at the end of B, S = 0
(no improvement) B is repeated with the smaller
step-size 02' Next the stop condition S ~ 0 is
tested. If S = 1 it is reset to 0, the 8 , N
are cleared and routine M repeats.

383

which are not continuous in time, Fourier analysis).
Acknowledgment
The author is indebted to Mr. J. Paul Landauer
of Electronic Associates, Incorporated, for information and suggestions.
References
1. Brooks, S. H.,"A Comparison of Maximum-Seeking
Methods /! Operations Research, 7, No.4, 1959.
2. Kinney, R., "A Model Adaptation Technique for
Computer Controlled Batch Chemical Process,"
M.S.Thesis, Case Institute of Technology,1960.

Initialization (not illustrated): It is convenient to initialize the digital system by
clearing all its flip-flops from a central control. At this time the operator can introduce
starting values for Ai' The hybrid program will
start as soon as the s?stem clock is turned on.
A non-repeating initialization routine is patched
to perform the following operations: (a) set all
flip-flops .which should be energized initially;
(b) calIon the RUN subroutine to calculate and
store the value E corresponding to the initial
parameter values;o(c) start the master routine of
the problem.

4. Box, G. E. P. and Wilson, K. B., Journal Royal

Equipment Requirements

6. Munson, J. and Rubin, A. 1., "Optimization by
Random Search on the Analog Computer," I.R.E.
Trans. EC-8, No.2, 200, 1959.

If no further rearrangements are carried out,
the following numbers of components are required,
where n is the number of parameters.
2n + 2 switches
2n + 4 analog memory units
5 comparators

On the analog side:

On the digital side:

11 GPFF
6

+ 4 [{-] QFF

50 AND/OR gates
1 counter
Conclusions
The addition of the digital expansion system
providing logic capability to the general purpose
analog computer will enlarge its capabilities as
an automatic computing device.
The less flexible relay and stepping-switch
arrangements used in the past are eliminated and
full use is made of the computing speed of the
analog computer. This alone brings within reach
problems, such as optimization, where computing
times were previously excessive in most cases.
The further addition of point storage in digital
form on delay lines will permit the use of serial
techniques for solution of integral and partial
differential equations. Problems of a statistical nature can be handled with a maximum of automatic operation. Many simpler auxiliary functions for GPAC's can be easily carried out (automatic scale changes, editing of graphical plots

3. Brunner, W., "An Iteration Procedure for Parametric Model Building and Boundary Value Problems," Western Joint Computer Conference,1961.
Statistical Society, B13, 1, 1951.
5. Lapidus, L., Shapiro, E., Shapiro, S. and
Stillman, R. E., "Optimization of Process Performance", A. I.Ch.E. Journal, 7, 288, 1961.

7. Follin, J. W., Emch, G. F. and Walters, F. M.
''Modification and Additions to the REAC," Project Cyclone Symposium II, p. 173, 1952.
8. Hansen, G. R., '~he Time-Sequence Controller
for Automatic Operation of the Electronic
Differential Analyzer," Project Typhoon Symposium III, p. 65, 1953.

DDA AND HYBRID COMPUTATION

384

SYMBOLS

[)

a
~

b
ab

negation

AND gate

at b

~----r---~ I state

b ___.....

a+b

'--_-.,. 0 state
R
OR gate
GPFF general purpose flip- flop
I

... SS

~~~~
I

--=...

SR
S

~~S

QFF quadruple flip - flop

~,.S

~~S

Ring
Figure 1:

Digital System Symbols

Counter

HYBRID TECHNIQUES APPLIED TO OPTIMIZATION PROBLEMS

385

ANALOG CIRCUIT

-Ai
PROBLEM
EQUATIONS

-E

HOLD

-E

~ ~
,--,---

IMP

=C>--

switch under
DIGITAL control

Figure 2:

Analog Computer Circuit

analOg

memory
~der DIGITAL
control
c.omparator
generating
DIGITAL
signal

.386

DDA AND HYBRID COMPUTATION

MASTER

EXPLORE

(\x x

Track

2 I" -.... , N I
\::;./
,,-.,.,111'\

EXPLORE
Start

--RUN

1-+ i

RUN

O-+ENHM

o=8 j

N+N

Track

1·8 i

6..... 0118 1, 1--+

0 ..... 0110, N I - - - - -..... ~

all x
~

0-+0

Figure 3:

, N-..N

Program Flow Diagram

O-+L
J....--......

end

HYBRID TECHNIQUES APPLIED TO OPTIMIZATION PROBLEMS

387

RUN

delay

~delaYH

delay

~end

PROCEED
I.... S

RUN

UP
DATE

I-+r

N
Track
'--------I

UPDATE

Hold Aio,E o;TrackAI,E,8E
I

~end

DDA A:-.JD HYBRID COMPUTATION

388

Su broutlne C

RUN
OPL

MODE

CONTROL

SL CL

' - - -....-

HOLD

COMP

ENHM

S
eS(I)

Hold

TRACK 8E

Figure 4:

Subroutine C.

RUN

8E+

HYBRID TECHNIQUES APPLIED TO OPTIMIZATION PROBLEMS

389

Subroutine D

UPDATE

SL CL

Track

Hold

A,E

Ao, Eo

Figure 5:

Subroutine D.

UPDATE

390

DDA AND HYBRID COMPUTATION

Subrout i ne A

EXPLORE AND STORE

clear

8An ON

i= n

~l
I
SH

LT~R

r-l

L J
~

8An
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