"*'"

byby

Kenneth R. Laughery

State University of New York at Buffalo

Kenneth R. Laughery

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COMPUTER SIMULATION OF SHORT-TERM MEMORY:

A COMPONENT-DECAY MODEL

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COMPUTER SIMULATION OF SHORT-TERM MEMORY:1

A COMPONENT- DECAY MODEL

2Kenneth R. Laughery

State University of New York at Buffalo

Prepublication draft of a chapter to appear in

J. T. Spence and G. H. Bower (Eds.), The Psychologyof Learning and Motivation: Advances in Researchand Theory. Vol. 111. New York: Academic Press.

This research was supported by Research Grant No. MH-11595 from theNational Institute of Mental Health, United States Public Health Service.

2Contributions to the development of the short-term memory model have beenmade by a number of people associated with the author during the past twoyears. Special thanks go to Patricia Fiero, Richard S. Cimbalo, Allen L.Pinkus, James C. Fell and Gilbert J. Harris.

11

TABLE OF CONTENTS

I. Introduction

11. The Model - An overview111. The Model - A Detailed Description 8

Q

A. Basic Units of InformationB. Basic Forgetting Mechanism 14

14C. The Memory Structures1. Long-term Memory 162. Short-term Memory l8

24D. Memory Processes '"*1. Noticing2. Item Recognition 313. Updating Item in STM 374. Checking Environment 425. Rehearsal6. Links and Order Information 507. Using Links 528. Responding 5£9. Recoding 55

E. Types of Errors that the Model Can Make 63

IV. A Sample Simulation 67

V. Some Simulation Results 79

A. Simulated Study Number 1: A General Experiment 79

B. Simulated Study Number 2: High vs. Low Auditory 86Similarity

VI. Discussion and Conclusions 89

A. Some Possible Extensions 9°1. Interitem Time Distributions During Input 902. Split Span Studies 923. Relative Recency Judgments 944. Free Recall 955. Delayed Recall 96

B. Some Possible Revisions 98

VII. References 103

FIGURE

LIST OF FIGURES

1. General Model of Human Memory System 2

2. Family of Curves Describing Decay Functions 15

(this figure shows 15 of the 30 decay

functions in the model)

3. Long-term Memory Structure 17

4. Short-term Memory Structure 19

5. Short-term Memory Structure for a Single Item 20

6. Subject Executive Routine - SI 277. Store Basic Component Routine - S2O 298. Short-term Memory Structure After Inputing 32

First Item (Letter X)

9. Net Sorting Routine - S4 34(Recognition or Discrimination Process)

10. Store and Update in Short-term Memory 39

Routine - S5U. Interitem Activity Routine - SlO12. Rehearsal Routine - SlOO 4613. Recoding Information in Long-term Memory 59

14. Serial Position Curves for 8 and 10 Item Sequences 87

iii

1

I . INTRODUCTION

The past few years have witnessed the development of several models

of human memory. Examples are Atkinson & Shiffrin (1968), Bower (1967),

Sperling (1967) , Waugh & Norman (1965) and Wickelgren & Norman (1966) . Themost generally accepted concept in the theories is that memory can best be

represented by three separate storage systems. The three parts of this

general model of memory are illustrated in Fig. 1.

The first of these systems is the sensory storage or very-short- term

memory, and is viewed as a peripheral or perceptual storage. There is

general agreement that information stored in this type of memory decays

with time and is lost in a matter of a few seconds or less (Averbach &

Coriell, 1961; Glucksberg, 1965; Sperling, 1960). Another type of memory,

short-term memory (STM), is the focus of these various models. Despite

general agreement that information is lost from STM (as opposed to loss

of access to the information) , there are two views as to the nature ofthis loss. One view is that information is lost as a result of decay; an

alternative is that STM has a limited capacity so that items are lost by

being replaced by new items entering the system. Choosing between these

alternative postulates is almost a matter of theoretical style, since the

issue has not lent itself to any clear-cut experimental resolution. Long-

term memory (LTM), the third type of storage, received relatively little

attention in the theoretical efforts cited above. It would appear, however,

that there is general agreement as to why information is not always recalled

perfectly from this permanent storage. The widely accepted view is that

what is lost is access to the information and not the information itself.

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The work reported in this paper represents an attempt to construct

a computer simulation model of human memory. It is a theory of the

average S. 3 The model represents the human at an information processing

level of description. At this level the human is viewed as having avail-

able a variety of processing mechanisms which can be employed to operate

upon information. The source of the information may be the external en-

vironment, such as a display device, or the internal environment (memory)

Like the other models already mentioned, a system consisting of the three

storage mechanisms is envisioned with the main focus on STM. The model

differs from the others, however, in one important respect: It describes

in complete detail a set of structures and processes that are intended

3As a rule, simulation models have either focused upon the behavior of an

individual S (e.g., Feldman, 1963; Laughery & Gregg,1962) or upon the

performance of an "average S" (e.g., Feigenbaum,1963). Clearly, these

are two separate approaches to theory construction. In addition to the

theoretical inclinations of the modeler, the decision as to which approach

to take is frequently determined by the nature of the task environment.

The tactic of building models for individual Ss (and hopefully finding

ways of pulling them together into a general model that includesappro-

priate parameters for representing the various individuals) has usually

been employed for simulating problem solving kinds of behavior. In these

tasks one can collect protocol data which provides a rich source of

information regarding behavioral processes. On the other hand, attempts

to construct models of the "average S" have generally involved tasks

which preclude getting protocols (the task would be grossly disrupted by

the procedure). The memory-span task is an example of a situation where

protocols would have a disrupting effect (except for post-sequence verbal

reports) .

4

to represent certain aspects of human memory.

While the model to be described purports to deal with the human

memory system, it is actually a simulation of performance in a particular

task. The task is the standard memory-span procedure, where a sequence

of items (such as digits) is presented, following which j5 reproduces as

many of the items as he can remember. Furthermore, the task is limited

to a vocabulary of 36 items; the 10 digits, 0-9, and the 26 letters of

the alphabet.

Although the model is presently limited to the memory- span procedure

and a 36 item vocabulary, it will be argued later that the model can be

expanded to simulate performance in many other memory tasks. Such exten-

sions will not require a restatement of the basic memory structures or

processes, but rather will involve only the addition of task-dependent

structures and processes to allow the model to perform in the different

situations. This distinction between basic and task-dependent structures

and processes is crucial. Indeed, one of the theses of this effort is

that a relatively few basic memory structures and processes can account

for performance on a variety of memory tasks-- the degrees of freedom in the

model are not larger than the points of fit.

One problem that has plagued computer simulation theorists is com-

municating to others the structures and processes that make up the model.

These models usually deal with relatively complex tasks, so the models

themselves have been complex. One issue is the level of description at

which the model should be presented. Presenting the program instructions

usually provides little help in understanding the theoretical concepts

underlying the model. On the other hand, attempts to describe the model

5

verbally generally result in some loss of precision. A compromise is to

describe the processes in the model in terms of flow charts which capture

the formal qualities of the model while communicating the logical com-

plexity .Another communication problem is the integration of the various parts

of the model. There are many parts of a simulation model, and it is im-

portant to understand how they fit together. A linear presentation of

these parts plays considerable havoc with the reader's intellectual

digestive system. A more appropriate procedure is to make two or three

descriptive passes through the model with each successive presentation

providing a more detailed description. The following model presentation

consists of an overview, a detailed description and an example of the

model's performance (a trace) on a specific sequence of items.

6

11. THE MODEL - AN OVERVIEW

In this section a general description of the model will be presented.

As already mentioned, the model represents performance in a memory- span

task where the item vocabulary consists of the 36 digits and letters.

The digits and letters, however, are not the basic units of information

in the model. The basic information units or components are a set of

visual and auditory features that define the visual and auditory dimen-

sions of the vocabulary items

Two types of memory, STM and LTM, are represented (the current version

of the model does not include a very-short- term memory). The LTM contains

the visual and auditory definitions of the vocabulary items and represents

S's permanent knowledge about the items. The STM is a series of memory

structures, each holding information about an individual item. This item

information includes the names of its auditory components, the times at

which the components were stored, and functions describing the decay of

the components

The basic forgetting mechanism in the model is a decay process. This

process is described by an exponential function which defines the probabilit

of retrieving a component as a function of length of time it has been in

STM. The components decay independently.

The flow of events in the model is as follows

1. A set of components (visual or auditory-representing the

presentation mode) are presented to S.

2. The S notices ("sees" or "hears") the set of components.

3. The S searches LTM and finds an item whose components match the

7

input (the item is recognized)

4. An STM structure is set up for the item with a substructure for

each auditory component. Each substructure contains the component's

name, the time it was stored and a function describing its decay.

5. If the next item has not been presented, the items already in STM

are rehearsed during the interitem interval. Rehearsal consists

of retrieving components of an item from STM, recognizing the item

by finding a match in LTM, and then updating the component sub-

structures in STM. Updating involves resetting the time and

changing the decay function so that the component decays at a

slower rate.

6. If after all items are rehearsed there is still time available

(a new item has not been presented), an attempt is made to recode

groups of items that are consistent with certain recoding criteria.

7. At specific points during the above activity S checks if a new

item has been presented, and if it has the process reverts back

to step 2.

8. When a special "respond" signal appears and is recognized (a 37th

vocabulary item) , control is transferred to a respond process

that attempts to recall (and output) the items.

9. When recall of a sequence is completed, the STM structures repre-

senting that sequence are erased. A new sequence is then begun

with nothing in STM. Thus, the model does not deal with proactive

or retroactive interference between sequences.

8

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111. THE MODEL- -A DETAILED DESCRIPTION

Two major parts of the simulation program can be distinguished-

data structures and routines. The data structures represent the long-

term and short-term memories. The routines represent the processes

available for operating on memory. These processes include taking in

information from the environment, storing it in memory, retrieving it

from memory, and outputting information to the environment. Other

routines represent processes such as rehearsal and recoding or chunking

Beyond this distinction between data structures and routines, two

basic concepts are fundamental to understanding the model. These model

concepts are a simulated clock and a window. The clock is essentially a

cumulative record of the time required by the various memory processes.

Underlying this concept is the assumption that the human is basically a

serial processor; he can perform only one cognitive process at a time,

and all processes require some amount of time to be carried out. With

the occurrence of each process, the clock is incremented by an amount

of time associated with that process. The time base is milliseconds.

The window represents the visual display or the tape recorder through

which information is presented to S. While the data structures and

routines are Intended to represent the human subject in a particular task,

the program also includes data structures and routines that are intended

to represent the experimenter. "Experimenter" refers to the human in

charge of the experiment as well as those pieces of equipment that are

9

part of the laboratory situation. In the model the window is a cell or

series of cells into which and from which the experimenter routines can

place and remove information. The experimenter routines monitor the

simulated clock and at appropriate times put information into or take

information out of the window. The S also monitors the window, and through

it the information is "seen" or "heard."

Given these two concepts, the model can now be presented in detail.

The presentation is divided into five sections; the basic information

units, the forgetting mechanism, the memory structures, the memory processes,

and types of errors the model can make.

A. Basic Units of Information

In addition to the 10 digits and 26 letters, there is a 37th item in

the model's vocabulary which is a signal to S that the sequence is complete

and it is time to recall. It represents an auditory or visual signal

occurring at the end of the input sequence

While the digits, letters and special symbol make up the vocabulary

of the simulated S, these are not the basic units of information with

which the model deals. Rather, the information units are visual and

auditory components or features that can be used to define the visual

and auditory dimensions of the vocabulary items. The auditory components

4No discussion of the experimenter data structures and routines will

be given since this part of the program contributes little to under-

standing the model.

10

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are named Pi, P2, , P43, and their definitions are presented inTable 1. The visual information components in the model are a set of 21

basic line segments and line relationships which include elements for

describing a standard version of the digits and letters. These visual

components are named VI, V2, , V2l, and their definitions are presented in Table 11.

Each of the vocabulary items, digits and letters, can be uniquely

defined by some combination of either the auditory components (which de-

scribe how the item sounds) or the visual components (which describe

what the item looks like) . These auditory and visual descriptions arepresented in Table 111. The visual and auditory descriptions of the

respond signal are special symbols (V24 and P44) that are not part of thebasic sets in Tables I and 11.

While the types of information units that can be stored in memory

involves a basic assumption about the memory system, the units that

actually do get stored is probably a function of the task environment.

It will be assumed in this model that only auditory components are stored

in and retrieved from STM. This assumption seems appropriate for repre-

senting performance on a memory-span task involving digits and letters.

5The standard version is the digits and letters produced by an IndustrialElectronic Engineering Company Binaview display. The reason for selectingthis version was that Binaview displays were used in all our experimentsinvolving a visual presentation.

11

Table I.

Basic Auditory Components

Component Name

PIP2P3P4P5P6P7P8P9PlOPllPl2Pl3Pl4Pl5Pl6Pl7PlBPl9P2OP2lP22P23P24P25P26P27P2BP29P3OP3lP32P33P34P35P36P37P3BP39P4OP4lP42P43

Phonetic Symbol

Pbtdkgfvc5

z/3vd3hmnQii

cmaoovvA

3-erwj1rciaxoiauou

Example

£aYbaytipdipcallgonefatvatthinthensuezooshoevisionchurchJLudgehatmayniplungeatitvacationpensatfatherallnotationpullpoolaboveaboveworkerworkerweyeslawrobaimhighboyloudopen

12

Tabic 11.

Description of Basic Visual Components

CharacteristicMane

VI

V2

V3

V4

V5

V6

V7

V8

V9

VlO

Vll

Vl2

Vl3

Vl4

Vl6

Vl7

VlB

Vl9

V2O

V2l

CharacteristicDescription

Vertical Left

Vertical Center

Vertical Right

Horizontal Top

Horizontal Middle

Horizontal Bottom

Full Positive Sloping Line

Pull Negative Sloping Line

Full Curve, Closed

Half Curve, Closed, Top

Pull Curve, Open Right

Full Curve, Open Left

Full Curve, Open Top

Half Curve, Open Left, Top

Half Curve, Open Right, Top

Half Curve, Closed, Bottom

Intersection

Two Lines Sloping Same Way

Part Positive Sloping Line

Part Negative Sloping Line

13

Table 111.

Auditory and Visual Definitions ofVocabulary Items

ocabulary AuditoryDefinitions

VisualDefinitionsItems

ABCDEFGHIJXLMN0PQRSTUVwXVZ0I23456789

Respond Signal

P39P2.P21P11.P21P4.P21P2lP24.P7P16.P21P23.P15P4OP16.P39P5.P39P24.P37P24.P18P24.P19P43P1.P21P5.P36.P30P26.P33P24.P11P3.P21P36.P30P8.P21P4.P31.P2.P37.P36.P30P24.P5.PHP35.P40P12.P21P12.P21.P38.P28P35.P31.P19P3.P30P9.P38.P21P7.P28.P38P7.P40.P8P11,P22,P5,PUP11,P24,P8,P32,P19P39.P3P19.P40.P19P44

V5.V7.V8V1.V14.V15VllV1.V12V1.V4.V5.V6V1.V4.V5V5.V11V1.V3.V5V2,V4 ,V6V4.V13V1.V20.V21VI,V6V1.V3.V20.V21V1.V3.V8V 9V1.V14V9.V11.V21V1.V14.V21V15.V16V2.V4Vl3V7.VBV7,V8,V19,V20,V2V7.V8.V18V2.V20.V21V4.V6.V7V11.V12V 2V6.V12V14.V15V2.V5.V18.V20V1.V4.V15V17.V20V4.V7V10.V17V3.V16V24

14

For other tasks, however, other types of units (e.g., visual or speech-

motor) may be appropriate.

The basic forgetting postulate in this model is that informationunits in STM decay in time. Clearly this is a basic assumption about

the memory system. Actually, the model contains thirty different ratesof decay that describe how information is lost. Each rate is described

by an exponential equation giving the probability that a unit of informa-

tion, a component, can be retrieved as a function of the length of timethat it has been stored in memory. The form of these equations is

where p is the probability that the component is retrieved, t is the

length of time the component has been in store, and A, B, C, are free

parameters .In the present model the C parameter, which represents the asymptote

is assumed to be zero; the A parameter, the probability of retrieval ofthe unit at time t = 0, is assumed to be 1. These assumptions leave thedecay rate, B, as the free parameter describing the decay function.

A subset of the family of curves, or decay rates, used in the modelare shown in Fig. 2 along with the value of the B parameter for each ofthe curves. The D's are the names of the routines that actually carry

out the calculations for that particular decay rate. The manner in whichthis process is incorporated into the model will be described later.

It is assumed that human memory can best be represented by a system

B. Basic Forgetting Mechanism

-Btp= Ac + C (^

C. The Memory Structures

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consisting of three separate storage mechanisms: very-short- term memory,

STM and LTM. For the model presented here, only STM and LTM are represented

Some additional comments will be made later regarding the development of

the model to include a very- short- term memory.

The LTM is represented by a structure which contains information that

is permanently available to S. In order to simulate the human in a memory-

span task consisting of sequences of digits and letters, LTM contains in-

formation about digits and letters that is relevant to this particular

task. In the model this information includes: (a) the visual components

that describe what the item looks like; (b) the auditory components that

describe how the item sounds; and (c) some information about how the item

may be combined with other items for recoding into larger chunks. This

recoding information will be described in Section 111, D, 9 where recoding

processes are discussed.

The LTM structure is a modified discrimination net (Feigenbaum, 1963)

The nature of the structure is shown in Fig. 3. It consists of a list

(LO) containing the names of all items in the vocabulary (LI--L37) . Each

In the model the vocabulary items are coded as Ll-L37, where Ll = A,

L2= B, L36 = 9 and L37 = the special respond signal. The reasonfor this code, as opposed to referring to them by their usual symbols

(A,B,C, etc.) is simply that the computer programming language (IPL-5)

does not permit the standard symbols to be used In this fashion.

1. Long-term Memory

17

AUDITORY COMPONENTSP39

- -

VISUAL

COMPONENTSV5V7VB

■— AUDITORYCOMPONENTS

P2P?l

VISUAL COMPONENTSVIVI4Vl5

AUOITORY COMPONENTSPI9

P4O

Pl 9

VISUAL COMPONENTSV 3VlB

L37(output signal)

AUDITORY COMPONENTSP44

VISUAL COMPONENTSV24

Flgur*- 3. I.otik-Uttii Memory Structure

18

item is in turn the name of a list that contains the names of two sub-

lists. The first sublist contains the auditory components that describe

the sound of the item's name. The second sublist contains the visual

components that describe what the item looks like. Hence, this list

structure, consisting of the main list of vocabulary items each of which

has two sublists containing the auditory and visual components describing

the item, represents the LTM. There is a third sublist containing

information about recoding, but discussion of that portion of LTM will be

deferred to a later section.

In this model STM has an unlimited capacity. The STM structure

consists of a number of memory cells

which holds all information about an

The cells are connected by links (to

order information. Actually, each M

(see Fig. 4) , ft. —M , each ofindividual item (a digit or letter) .be described later) which represent

location is not a single cell but a

large number of memory cells which are organized into a list structure.

The M location contains the name of the memory structure which in turn

contains all of the information about that particular item. The memory

structure for an item is shown in Fig. 5.

In Fig. 5 the name of the structure is a list of the auditory com-

An important point here is that the number of cells, n, is not aparameter of the model, but the number of items to be remembered. Thatis, the model simply uses as many memory cells as needed to storeinformation about the items.

2. Short-term Memory

19

i.

ITEMMn

Figure 4. Short-term Memory Structure

20

Figure 5. Short-term Memory Structure for a Single Item

21

v.

ponents that describe the item. More precisely, it is a list of names

of sublists each of which contains three types of information: (1) the

name of the auditory component, a P unit; (2) the clock time at which

that component was stored in STM; and (3) a decay function, a D, speci-

fying the exponential relationship between the probability of retrieving

the component and the length of time the component has been in a store.

At this point, two important assumptions of the model should be noted:

First only the auditory components of an item are assumed to bestored

in STM; and second, the decay of the individual components of an item

is assumed to occur independently.

In the initial conception of the model both auditory and visual

components were stored in STM. A number of studies have shown that the

auditory dimensions of items plays an important role in STM (e.g.,

Cimbalo & Laughery, 1967; Conrad, 1964; Laughery, 1963; Laughery &

Pinkus, 1966; Wickelgren, 1965a). However, other evidence has appeared

which indicates that in simulating performance in a memory-span task for

digits and letters, visual components should not be a part of the

information in STM (Baddeley, 1966; Cimbalo & Laughery,1967; Laughery,

Harris & Ulbricht, 1967). For example, interference and confusions

among items being recalled seem to follow their auditory, not their visual

similarities. As a result of these studies the model was modified so that

8

22

only auditory components are a part of STM.

Another line of evidence is relevant to the question of "What is

stored in STM?" Hintzman (1965, 1967) has reported data which indicate

that speech-motor or articulatory components may also be important. Some

comments on this alternative and the possibility of "distinctive features

will be made later in the paper.

The second characteristic of STM in the model to be noted concerns

the independent decay of the auditory components. As indicated in Fig. 5

each component has a decay function specifically associated with that

particular component. The decay function may be the same or different

for various components. However, it is assumed that the rate at which a

component decays does not depend upon the nature of the other components

nor upon the specific decay functions assigned to other components.

Bower (1967) suggested two alternative possibilities as to how com-

ponents might be forgotten. The first alternative was called "hierarchical

loss of components." The idea here was that the various components could

be ordered in importance and the retention of a component would vary

directly with its importance. Furthermore, components at one level in

the hierarchy would not be lost until the components at the lower levels

BAs8As mentioned earlier, the decision to use only auditory components inSTM is task dependent. It is not suggested that visual, articulatory

or some other dimension of information has no role in STM; but rather,

in this particular task - the memory span for digits and letters - onlythe auditory dimension is relevant.

23

had been lost. The second alternative suggested by Bower was called "in-

dependent loss of components." Here, the components are equally important

and show equal resistance to forgetting. He assumed that the components

in the independent loss alternative are forgotten at the same rate.

The process suggested here is independent loss but with possibly dif-

ferent rates for the several components. In other words, some will decay

more quickly than others but this rate is independent of the rate at which

others decay. Incidentally, the decay process does not describe the pro-

bability that a component is lost forever. Rather, it describes the

retrieval probability at a particular time. For example, if a component

is not retrieved during an attempted rehearsal, it may still be retrieved

during a later rehearsal or recall (of course, at a later time the pro-

bability would be even lower) .Another issue raised by Bower (1967) regards the value of the com-

ponent after its initial value has been forgotten. Bower offered two

possibilities: the value reverts to a null state (it simply goes away);

or, the forgetting consists of replacing the original value of the component

by some incorrect, non-null state. The null-state idea is similar to the

decay notion of forgetting while replacement is more consistent with

interference. In the present model when a component is forgotten it reverts

to the null state

Finally, it seems appropriate at this point to note an alternative

forgetting mechanism that was considered in the initial formulation of

the model. Instead of having the decay function represent the probability

of retrieving a component as a function of how long it has been in memory,

the function could represent the relationship between strength of the

24

component and the time in store. By defining a strength threshold below

which the component is not retrieved and above which it is retrieved,9

the same all-or-none retrieval of the component would be represented.

The routines representing the memory processes will now be described

These are the processes available to S for taking in information from

the environment, storing information in memory, retrieving information

from memory, and outputting information to the environment. Flow charts

will be used to communicate the flow of events in the model. The aim

here is to indicate what the model says about these memory processes.

After this description of the processes, a sample simulation will be

presented.

The routines that comprise the simulation program are hierarchially

organized. A general routine at the top of this hierarchy is referred

to as the Model Executive Routine (El) , and it directs the overall flow

qThe introduction of retrieval thresholds would bring the model intocontact with the recent work on decision processes in STM (the theoryof signal detectability) by Wickelgren & Norman (1966). However, theapplication of decision theory to memory does not require a continuousstrength assumption since Bembach (1967) has proposed a model basedupon decision theory that assumes a finite-state memory (two states--available and unavailable). We intend to explore these alternativesin future versions of the model.

D. Memory Processes

25

L

of events in the model. This routine executes a series of subroutines

which in turn have subroutines, and so forth. The Model Executive Routine

contains subroutines which represent the experimenter, the equipment and

the subject. The experimenter routines are responsible for setting up

the sequences according to specified criteria (e.g., the types of items,

digits or letters, in the sequences and the rate at which they are to be

presented), for monitoring the clock, and for placing items into the win-

dow and removing items from the window at the appropriate times. In

short, these routines conduct the experiment.

A number of model routines that represent S will be described in

detail, and Table IV presents the program name and a descriptive title

of each. The routine with which this discussion will begin is a sub-

routine of El and is referred to as the Subject Executive Routine (SI).

The flow chart in Fig. 6 presents SI. At the time this routine is

entered the simulated clock has been set to zero and an experimenter

routine has put the first item into the window. The SI routine is

entered at the beginning of a new sequence of items and, as can be seen

from the flow chart, exited when that sequence has been output by S.

Before each new sequence is presented to the simulated S, the clock is

reset to zero and the memory structures set up for the previous sequence

are erased. This procedure is essentially a present boundary condition

of the model and precludes its representing any proactive or retroactive

interference that may occur between sequences. It is therefore, a model

of performance on single "representative" sequence

An important characteristic of the model concerns the nature of

26

Table IV.

Program Name and Descriptive Title of Model Routine

Program Name

El

SI

S2

S3

S4

S5

S6

SlO

Sll

S2O

522

S4O

S4l

542

S5O

552

SlOO

SlOl

SlO5

SllO

Descriptive Title

Model Executive

Subject Executive

Input Stimulus

Is a New Item in Window?

Net Sorting

Store and Update in Short-term Memory

Respond

Interitem Activity

Find Location (M) of Next Short-term

Memory Structure

Store Basic Component

Store Link Substructure

Select Item

Generate List of Consistent Items

Generate List of Items Consistent With

Most Components

Retrieve Auditory Components of Item

from Dictionary

Update

Rehearsal

Retrieve Remembered Components of an Item

Is Rehearsal Continued?

Recoding

27

L

Figure 6. Subject Executive Routine - SI

y

28

the item information that has been placed in the window by the experi-

menter routines. This information is the visual or auditory components

which describe the item being presented. If the simulated experiment

involves a visual presentation mode, the window will contain some com-

bination of visual components (V's). If the presentation mode is

auditory, some combination of auditory components (P's) will be in the

window. For example, if the first item is the letter X and the pre-

sentation mode is auditory, the window will contain P24, P5 and Pll

(see Table III) .1. Noticing

From Fig. 6 it can be seen that the first process is for S to

notice or take in the information in the window. What happens depends

upon the mode of presentation being simulated. If the presentation is

auditory (the components are P's), a STM structure is set up in Ml for

each of the components of the first item. If the presentation is visual

this structure is not set up immediately since visual components are not

stored in STM. As indicated in Fig. 6, the Input Stimulus Routine, S2,

is responsible for carrying out this input process.

With auditory presentation the STM structure is set up in the fol-

lowing fashion. In serial order, each of the components is copied from

the window and combined with a time

list. The name of the list is then

the structure stored in Ml (see Fig

individual component is carried out

tag and decay function to make up a

added to another list whose name is

5) . The storing in memory of eachby a Store Basic Component Routine,

S2O. The flow chart for S2O is presented in Fig. 7. This process works

in a straightforward manner: a new sublist which will represent this

29

if/ure 7. Store K'ihlc Component Koutlnc - S2Oi'

30

component is generated; the name of the component is taken from the window

and placed on this sublist; the value of the simulated clock at this

instant is copied and added to this sublist; and a decay function asso-

ciated with this particular component is retrieved and added to this

sublist. The Store Basic Component Routine is a process that takes time

(a time-charge process). Consequently, at the end of the process an

increment of time is added to the clock. This time increment is one of

the basic time parameters in the model. In most of the simulation runs

carried out to date a value of 10 milliseconds has been assigned to this

parameter. (The reasons for using 10 milliseconds will be discussed

later.)

The manner in which decay functions are associated with specific

components is also straightforward. The model has a dictionary containing

the various auditory and visual components and an associated decay rate

(B constant) which describes the decay for that component when it is first

placed into STM. (In the current version of the model, of course, the

visual components do not get put into the STM) . Hence, the Store BasicComponent Routine simply retrieves from the dictionary the decay function

associated with the particular component and adds it to the sublist. As

indicated in Fig. 2 the model contains a number of decay functions which

differ in terms of the decay rate (the B constant) . Actually, any one offive different decay processes, those with B values of 0.107, 0.129, 0.160,

0.208 and 0.269, have been used as the initial values of the decay process

for the different components. The reason for assigning different decay

rates to different components is based upon some ideas expressed by

1

31

Wickelgren (1965) . Wickelgren noted that intrusion errors in the memory-span task tend to have an auditory component (a phoneme) in common with

the correct item. He further noted that some auditory components account

for more of these acoustically similar intrusions than others, and that

this difference was related to the pronunciation time of the phoneme.

Using this idea, the auditory components in this model were classified into

five categories according to their pronunciation time as reported by

Fletcher (1953) . The decay rates were then associated with the variouscomponents in the dictionary such that the longer the pronunciation time

of the component the slower the decay rate.

Once the sublist representing the first component has been set up and

added to the STM structure, the second component is copied from the window,

a similar component substructure is set up, and this substructure added

to the STM. This process repeats for each of the auditory components in

the window. When all of the components representing the first item have

been put into STM, S2 terminates. For example, if the first item was an

X in the auditory presentation mode, the STM structure will contain the

information indicated in Fig. 8. The

different component substructures, 0,

of the processing as well as the fact

added to the clock at the end of each

time tags associated with the

10 and 20, reflect the serial nature

that the time increment that was

execution of the Store Basic

Component Routine, S2O. Also, because the time increment is added to the

clock at the end of the process, the value of the clock would be 30 when

the Input Stimulus Routine, S2, is finished.

2. Item Recognition

The only thing the model has simulated thus far is S noticing the

32

STRUCTURENAMEMl

COMPONENTSUBSTRUCTURE

COMPONENTSUBSTRUCTURE

COMPONENTSUBSTRUCTURE

Figure 8. Short-term Memory Structure After Imputing First item

(Letter X)

»

33

k

item in the window. This noticing does not include what would normally

be thought of as S recognizing the item. He has merely "heard" the item.

The next step in the model (the second box in Fig. 6) is the Net Sorting

Routine and represents a recognition or discrimination process. In gen-

eral the process consists of taking a set of components and retrieving

from the discrimination net (LTM) a vocabulary item on the basis of these

information components. The flow chart in Fig. 9 describes the Net

Sorting Routine, S4. There are two inputs to this routine: a set of

components (V's and/or P's); and a signal indicating if no response, a

blank, is a legitimate alternative in the retrieval process. The out-

put of the Net Sorting Routine is the name of a vocabulary item if it is

not a blank or an appropriate signal if it is a blank. The reason for

the input signal regarding the legitimacy of a blank is to allow the

model to represent various task-dependent processes. For example, in

the response phase of the task, when S is attempting to recall the sequence

of items, the task may require that he output as many items as were input.

In this situation the Respond Routine, which also uses this Net Sorting

Routine, would signal that a blank is not a legitimate alternative, and

the model, like S, must guess (if the item ia not remembered). In other

parts of the model using the Net Sorting Routine, such as the rehearsal

process, a blank may be legitimate alternative.

From Fig. 9, the first step in the Net Sorting Routine isa sub-

routine, S4l, which generates a list of all items in the net that are

consistent with the input components. The consistency rulehere is that

if an item contains all of the components in the input it is considered

consistent. In the example where the first item isthe letter X and the

34

Figure 9. Net Sorting Routine - S4(Recognition or Discrimination Process)

1

Ii

35

L

input components are the three auditory components which make up the

letter X, the S4l routine would generate a list that contained only the

letter X. However, if the item was the letter E (whose auditory descrip

tion consists of the single phoneme P2l) the S4l routine would generate

a list of items consisting of all of the letters or digits that contain

this particular phoneme (BCDEGPTVZ3) .The second step in the Net Sorting Routine asks the question "Is the

list of consistent items empty?" It is possible under certain conditions,

which will be described later, that the input to the routine may be a

set of components that is not consistent with any vocabulary items. When

such a situation occurs the list of items generated by S4l is empty, and

the model goes to routine 542 which generates a list of items that match

the greatest number of input components. For example, if there are three

input components, and no item is consistent with all of them, 542 searches

for items that are consistent with any two of the input components and

puts them on the list. If none of the items are consistent with two

components, 542 gathers up those items consistent with any one component.

At this point a list of consistent items will have been generated

and the model proceeds to the question "Is there only one item on the

list?" If the answer is YES, the input components will have defined a

unique item, and that item would be output by S4. Since this recognition

process (Net Sorting) is one of the basic processes in the model, it has

an associated time charge. This time increment is another parameter of

the model and is added to the clock value as the last step in the S4

routine. In most of the simulation runs to date a value of 100 milli-

36

seconds has been assigned to this time parameter. (The basis for using

100 milliseconds will be discussed later.)

Returning to Fig. 9, if the answer to the question "Is there only

one item on the list?" is NO, another question is asked "Does the set

of input components exactly match a single class of components of any

vocabulary item?" For example, if the iraput components were P24 and Pll,

the list of consistent items generated by S4l would contain both S and X.

The two imput components, however, exactly match the auditory description

of S but not X. Hence, the answer to the question would be YES and the

letter S would be output. Similarly, if the input component was P2l,

the items BCDEGPTVZ3 would be on the list. The output would be the letter

E because its auditory description exactly matches the single input com-

ponent (this rule creates a particular problem for the model which will

be described later) . Note that an exact mntch with a single set of com-ponents (auditory or visual) of an item is a second way that the input

components define a unique vocabulary item.

The remainder of the Net Sorting Routine deals with the situation

where the input components do not define a unique item, the NO branch

from the last question. At this point a Select Item Routine, S4O, is

executed. Since the procedures in S4O are straightforward, its flow

chart will not be presented. Essentially what happens is the following.

If the input indicates that a blank output is legitimate, and if the

list of consistent items contains 10 or more (an arbitrary number at this

stage in the development of the model), a blank signal will be output.

On the other hand, if there are 9 or less items on the list, or a blank

is not a legitimate alternative, the S4O subroutine selects one at random

37

L

The last step in this branch of routine S4 is to increment the clock

by a time value associated with this phase of the process. The time in-

crement added under these conditions is not the same parameter as the

time increment when the imput components define a unique item (the value

of that time increment was 100 milliseconds). When a unique item is not

defined by the input, some sort of decision process (represented by S4O)

is presumably added which will cause the overall process to take longer.

Hence, the value of the time increment in the branch of the routine con-

taining the additional selection process will be longer than the time

charge when a unique item is defined. Various times have been assigned

to this parameter in the simulation runs to date, with 300 milliseconds

being a typical value.

After the Net Sorting Routine, the next step in the Subject Executive

Routine, Fig. 6, is the question "Was the item the respond signal?"

(Remember that the respond signal is one of the items in the discrimination

net and it will be uniquely defined when theappropriate component appears

in the window.) If the answer to this question is YES,control will be

transferred to the Respond Routine, S6. Theprocedures in the Respond

Routine will be discussed later. If the output of the Net Sorting Routine

is not the respond signal, control will be transferred tothe Store and

Update in Short-term Memory Routine, S5.

In this branch of the Subject Executive Routinethe possibility that

the output from the Net Sorting Routine was a blank isnot considered. The

reason is that in this branch there is no possibility thatthe blank

alternative would have been selected. The execution ofS4 has occurred

3. Updating Item in STM

38

immediately after a new item has appeared in the window, and as long as

the item is in the window and S notices it he will not fail to recognize

it. In other words, all of the components of the item are available as

input to the Net Sorting Routine and thus leads to recgonizing a unique

and appropriate item. The possibility of a blank output occurs under

other conditions which will be described shortly.

When an item has been retrieved from the discrimination net, its

auditory components are added to the STM structure for that Item by the

S5 routine. If these components are already stored in the STM structure

(as they would have been in this case by the S2 routine) , then the informa-tion regarding these components will simply be updated.

The manner in which the Store and Update in Short-term Memory Routine,

S5, proceeds is shown in Fig. 10. The inputs to this routine are the

location of the STM structure where information about the item is being

stored (one of the M' s) and the name of the item. In the example mentioned

earlier if S5 is updating the first item in the sequence, X, these inputs

would be Ml and X (actually, this latter input will be L24, the programcode for X) .

From Fig. 10, the first thing that happens in S5 is the execution of

a subroutine, SSO, which takes the name of the item to a dictionary and

retrieves the auditory components that make up that dimension of the item

(for the letter S these are P24, P5 and Pll) . The next step is a question"Is there another component?" which is simply the first step in a loop.

Each of the components on the list generated by SSO are taken one at a

time and dealt with. After all of the components have been handled the

answer to this question is NO and the routine is exited. Initially, the

39

Figure 10. Store and Update in Short-term Memory Routine - S5

40

answer to the question is YES since none of the components have yet been

considered. The first component is then taken from the list and the STM

structure scanned to determine if this component already exists in the

structure. In the present example the auditory components of the letter

X will have already been stored in the STM structure named in Ml, and the

answer to this question will be YES. There are other circumstances, how-

ever, where the answer may be NO. For example, if the presentation mode

in the experiment is visual, the Input Stimulus Routine, S2, does not set

up the STM structure for the item, since the auditory cues are not yet

available. Indeed, when the presentation is visual, the item must be

recognized in LTM and the auditory cues retrieved before anything can be

stored in the STM structure. Under this condition auditory components

of the new item would then be set up along with time tags and decay functions

in the STM structure by routine S2O in the manner previously described.

Note that when the presentation is visual, the auditory components stored

in STM represent a secondary code of the imput stimulus (cf. Bower, 1967).

However, when the presentation is auditory the stored components represent

the primary code of the stimulus. There are other situations in which

the components may not already exist in the memory structure. These

situations arise during the rehearsal and will be mentioned when that

process is discussed.

If the component already exists in the memory structure, control is

transferred to the Update Routine, 552. The Update Routine makes two

changes in the memory for that component. First, it replaces the time tag

in the component substructure with a copy of the current value of the clock.

In other words, the decay of the component starts anew. The second change

41

L

concerns the nature of the decay function. As indicated in Fig. 2, there

is a family of decay functions in the model such that the various functions

differ in terms of the rate of decay. There are 30 different functions in

all. When a component is updated its decay function is replaced by a func-

tion whose rate of decay is the next slowest in the set. This change repre

sents learning in the model.

There is an additional point worth noting about the change in the

decay rate that occurs during updating. As mentioned, the Updating Routine

simply selects the function with the next slowest rate. This updating pro-

cedure is also going to occur duringrehearsal, which means that the decay

function for a component may be updated many times. However, the amount of

change between functions is not constant. The differences between the slower

decay rates is less than between the faster rates.In fact, these differ-

ences are described by an exponential function also. The result of this

procedure is that the first rehearsal contributes more to remembering an item

than the second rehearsal, which contributes more than the thirdrehearsal,

etc. This change in decay rates representsa fundamental assumption about

the memory system

The Update Routine is another ofthe basic processes in the model.

Like the other basic processes, each time theUpdate Routine is executed

a time increment is added to the clock. Sincethis process is in some

sense a storage process, the time chargeassigned to it in the runs obtained

to date has been the same as the time for the StoreBasic Component Routine,

S2O. in most of the runs the value has been 10 milliseconds.

When the S5 routine is complete, apoint has been reached where the

simulated S has noticed the item in the window,recognized it as something

42

with which he is familiar and set up an appropriate STM structure for the

item. In the case where the letter X was presented and was the first item

in the sequence, the time on the clock at the end of S5 would read 160

milliseconds (30 milliseconds for the subroutines executed by S2, 100

milliseconds for the net sort in S4, and another 30 milliseconds for the

updating in S5) . As indicated in the Subject Executive Routine, Fig. 6,the next step in the process is routine S3 which asks the question "Is

a new item in the window?"

At this point in the discussion there are another two characteristics

of the model that must be clarified: When and how S monitors the window;

and, the manner in which the experimenter routines interrupt to make

changes in the window. Earlier the point was made that Sis viewed as a

serial processor. With respect to noticing new items in the window, there

are at least two procedures which might be adopted that seem consistent

with the serial assumption. The first of these procedures assumes that

S is interrupted, regardless of what he is doing, at that instant when a

new item is placed in the window. The second procedure assumes that S

actively checks the window at frequent intervals. In the second alterna-

tive, S's sequence of behavior would be interruptable only at these check-

points. The procedure adopted is the second, and the rule for when these

checkpoints will occur is that S will look for a new item in the window

every time he has finished processing a single vocabulary item. This

processing may involve taking in and storing a new item or rehearsing items

that have already occurred. Thus, in Fig. 6, the window will be checked

after the S5 routine has been executed.

4. Checking Environment

43

i.

The second point concerns when the experimenter routines make changes

in the window. The procedure is quite straightforward. Each timeS

is about to check the window to see if a new item hasoccurred, an experi-

menter routine is first executed which checks to see if any window changes

should have occurred. If so, the changes are made. More precisely, this

experimenter subroutine is executed as a first step in routine S3

The question as to how S knows that an item in the window is new is

essentially finessed in the present model. In short, a signal is output

by the experimenter routine indicating whether or not the item inthe

window represents a change since the last timeS monitored the window.

Routine S3 simply senses this signal. Also, routine S3 is a time charge

process and has a time parameter indicatingthe value added to the clock

at the end of the routine (10 milliseconds in most runs) .The next step in the Subject Executive

Routine depends upon whether

or not a new item has occurred in the window. If thepresentation rate

in the experiment is very fast(e.g., 10 items per second), the answer to

this question would be YES and the simulationwould branch back to the

first box in Fig. 6, Input Stimulus,S2. If, on the other hand, the

interitem interval is longer than the time consumedby the basic time

charge processes so far executed (160 milliseconds in thecurrent example) ,

control will be transferred to the Interitem Activity Routine, SlO.

The interitem Activity Routine is anattempt to simulate what S does

between taking in one item andwaiting for the next item to appear in the

window, in this model there are two types ofactivities that occur in this

interval, rehearsal and recoding. The general procedureduring the Intcr-

5. Rehearsal

44

item period is shown in Fig. 11. First, the model attempts to rehearse

all of the items that have occurred thus far, routine SIOO. The number

of items rehearsed in this model is a function of the time available for

rehearsal. If there is still time remaining after all items have been

rehearsed (a new item has not yet occurred in the window) , an attemptwill be made to recode or chunk items into larger units, routine SllO.

If after the recoding process has been executed time still remains, con-

trol will branch back to the Rehearsal Routine again. In both the Rehearsal

and Recoding Routines the simulated j> checks the window to see if a new

item has occurred each time an item has been rehearsed or considered in

the recoding process.

The nature of the rehearsal process, routine SlOO, is described by

the flow chart in Fig. 12. The first step in the process is to go to

the location of the first STM structure, Ml. In this model the simulated

S^ always knows the location of the first item--he may not remember what

the first item is, but he knows where to look for it. This knowledge

makes Ml an anchor point (Feigenbaum & Simon, 1962) . The next step isto execute routine SlOl which examines the memory structure in Ml and

retrieves all of the components that can be remembered. The procedure

in SlOl is to consider the components one at a time and determine which

This time-based procedure is different from the procedure proposed byAtkinson & Shiffrin (1968) . They propose a rehearsal buffer with acapacity to regulate the number of Items rehearsed.

45

L

lM X ..re 11. Interitem Activity Routine - St()

46

Figure 12. Rehearsal Routine - SI OO

47

can be remembered. This determination is made by subtracting the time

value associated with the component from the current value of the clock,

which results in the length of time the component has been in memory

since being stored or last updated. This time value is then used by the

exponential decay function associated with the component to compute a

probability that the component is remembered. The process then generates

a random number between 0 and 1, and on the basis of the random number

decides that the component is or is not remembered. For example, if the

item has been in store 1 sec. and the probability of retrieval computed

by the decay function is .80 and the random number generated is .65, the

component will be remembered. If the random number is .88, the component

would not be remembered. The SlOl routine is the basic retrieval process

in the model. Each time it is executed a time increment is added to the

clock The value of this parameter in most runs has been 10 milliseconds.

The remembered set of components output by SlOl is then provided as

input to the Net Sorting Routine, S4 in Fig. 9, which attempts to retrieve

an item that is consistent with these components. As indicated in the

third block in Fig. 12, a blank is a legitimate alternative in the Rehearsal

Routine. In the example, the SlOl routine would have retrieved some number

of auditory components of the letter X from Ml (probably all of them since

very little time has lapsed since the updating) and sorted them in the

discrimination net. The next question is whether or not the output of

the S4 routine is a blank.

From Fig. 12, if the result is not a blank (i.e., an item is retrieved

from the net), the auditory components which make up the retrieved item

are added to or updated in the short-term memory structure by routine S5.

48

If the S4 output is a blank the S5 process is skipped.

The next step in the rehearsal process is to execute the Find Location

of Next Short-term Memory Structure Routine, Sll. Having rehearsed the

first item in the sequence, X, the model will now attempt to find the item

that followed X in the sequence. Since in the example no item has yet

occurred following X, a discussion of Sll will be delayed briefly. It is

sufficient to note here that Sll is capable of sensing the fact that the

last item rehearsed was the last item presented.

At this point in the Rehearsal Routine the simulated S has finished

rehearsing a single item. Consistent with the rule cited earlier, the

window is now checked to determine if a new item has occurred. The S3

routine executes the experimenter subroutine which checks the window and

makes any appropriate changes. If a change does occur, the S3 routineoutputs a YES and the Rehearsal Routine is terminated. Control is thentransferred back to the SlO routine, Fig. 11, which asks the question "Is

activity continued?" The fact that a new item has appeared in the window

results in a NO answer to the question which in turn causes the Interitem

Activity Routine, SlO, to be exited. Control then reverts to the SubjectExecutive Routine, Fig. 6, which executes the S2 routine taking in thenew item.

Back at the Rehearsal Routine, Fig. 12, if a new item has not appearedin the window the question "Is rehearsal continued?" is asked by routine

SlO5. The answer to this question is determined in a straightforwardfashion. If any of the items presented so far have not been rehearsed(a fact which Sll has determined), routine SlO5 outputs a YES. Control

49

in the Rehearsal Routine then transfers back to the SlOl routine which

attempts to retrieve the components of the next item to be rehearsed. In

this fashion the Rehearsal Routine continues to rehearse items until one

of two conditions occur; a new item appears in the window, or all of the

items presented so far have been rehearsed. If all items have been re-

hearsed the Rehearsal Routine is exited. Control is transferred back to

the Interitem Activity Routine, Fig. 11, and the question "Is activity

continued?" is asked. Since rehearsal is finished but no new item has

occurred in the window, the answer to the question will be YES and the

Recoding Routine, SllO, will be executed.

In the example where only the letter X has been presented, the Re-

hearsal Routine is exited immediately after rehearsing the X. If no new

item has yet occurred in the window the Recoding Routine is executed.

The Recoding Routine, which will be described in detail later, notes

that only one item has been presented and is exited quickly. If a new

item still has not appeared in the window, control is transferred back

to the Rehearsal Routine which again rehearses the letter X. The result

of this procedure Is that the letter X continues to be rehearsed until

a sufficient amount of time passes and a new item occurs in the window.

When the new item appears control is transferred back to the Subject

Executive Routine which, as described above, takes in the new item by

executing routine S2.

The S2 routine now creates a new memory structure whose name is

stored in M2. Since the presentation is auditory, component substructures

are set up for each auditory component of the new item. Each of these

substructures contains the name of a component, the clock value when that

50

component was stored and an associated decay function. At this point the

last characteristic of the STM structure will be described.

6. Links and Order Information

Referring back to Fig. 5, it can be seen that in addition to the

substructures for each of the auditory components making up the item,

there is another substructure that is a

This substructure is referred to in the

substructure contains information about

were presented. The manner in which it

part of the memory for the item,

model as the link. The link

the order in which the items

works is quite straightforward.

Each time a new item occurs the S2 routine, in addition to setting up the

auditory component substructures for the new item, goes back to the structurefor the previous item and adds to it information about where the next item

is being stored. Specifically, the information added to the structureincludes the location of the new structure (in this case, M2 ), a time tagwhich is the current value of the clock, and a decay function which defines

the rate at which the link will be lost from memory. This link information

is added to the memory structure by a separate subroutine (522) of S2 inmuch the same fashion that subroutine S2O (see Fig. 7) creates substructuresfor the component information. The 522 subroutine is considered a basicprocess in the model and has the same time parameter as the S2O subroutine.In other words, this single parameter defines the time charge for creatingcomponent substructures in memory (S2O) , creating link substructures inmemory (522) and updating these substructures (552) .

From the above discussion, it can be seen that the model distinguishesitem information from order information. This distinction obviously providesa mechanism that will allow the model to produce one of the most common

51

11findings of the memory-span procedure—the order error. An order

error occurs when S recalls the correct items but in the wrong sequence.

The distinction between order and item information is not new; both Brown

(1959) and Crossman (1960) made the distinction to account for the order

error. The decision to introduce a decay process to account for the loss

of order information is supported by results reported by Wickelgren (1967) .

are alternative mechanisms that might be considered to account

for order errors. One possibility is simply to store an input time tag

with the item information (Yntema & Trask, 1963) . This time tag wouldrepresent the time when the item was input and would not be changed by

rehearsal. The recall procedure would involve scanning the cells and

outputting the items on the basis of the input time tags. The

availability of these tags might decay, thus producing the possibility

of order errors. Conrad (1965) offers a second alternative which is

simply to have the items stored in an ordered set of bins (memory

cells) . He argues that transposition errors can be accounted for onthe basis of item errors substituting for each other. His argument,

however, requires two additional assumptions: (1) can scan the

memory cells containing the items in order (which reflects the input

order); and (2) when an item is not remembered, a substitute will be

selected from a set of alternatives that is relatively small and consists

primarily of recent items. (Incidentally, it will become clear later

in the description of the Sll routine that the fact that the items are

stored in a sequence of cells called Ml, M2, etc. has nothing to dowith the order information. The cells could be filled randomly

(M5, M2, MB, etc.) --so long as the location of a new item is linked tothe memory structure of the previous item.)

52

Returning to the Subject Executive Routine, Fig. 6. After the new

item is input, its components are sorted through the discrimination net by

routine S4. The output of this routine is the name of the new item, and

the question is asked "Is this item the respond signal?" If the answer

is NO, the S5 routine updates all of the auditory components in the memory

structure for the new item, stored in M2. At this point the window is

checked to see if another new item has occurred, and, unless the pre-

sentation rate is quite fast, the answer is NO. The Interitem Activity

Routine, SlO, is then executed again.

Rehearsal Routine, SlOO (see Fig. 12)

SlO begins by executing the

Rehearsal starts with the structure

in Ml which for this example consists of the components of the letter X.

The SlOl routine retrieves as many of these components as can be remembered

and these in turn are sorted through the net by S4. If the X is remembered,

the components in the memory structure are updated by S5. Control is then

transferred to the Find Location of Next STM Structure Routine, Sll, which

can now be described in detail.7. Using Links

The Sll routine is capable of doing three things. First, it looks

at the memory structure for the item just rehearsed and attempts to find

the link information. If there is no link structure associated with thisitem, the Sll routine outputs a signal indicating that the item just re-

hearsed is the last item taken in (the situation that was mentioned earlier)

If a link structure does exist, Sll proceeds to its second step; namely,

it attempts to retrieve the location where the memory structure for thenext item is stored, it does this by going to the link structure and re-

trieving the time tag, subtracting this time tag from the present value

53

of the clock to determine how long the link information has been in memory,

using this time in the decay function to calculate a probability of re-

trieval generating a random number and deciding whether or not the next

location (M 2in the example) is remembered. (Notice that the specific

name of the next location, M2, has nothing to do with whether or not it

is remembered.) If it is remembered, the location is output and the link

structure is updated. The updating is much the same as updating one of

the component substructures. The time tag is reset to the current value

of the clock, and a new decay function representing a slower decay rate

is placed in the link structure. The third phase of the Sll routine

occurs when a link structure exists but its name is not remembered.

Under these circumstances all the STM locations, M's, containing memory

structures are scanned, and those that have not yet been rehearsed during

the current rehearsal process are retrieved. One of these locations is

then selected on a random basis. In this phase of Sll no updating occurs;

also no new link is formed between the previous item and the randomly

selected location.

The last step in the Sll routine is a time charge. Actually, there

are two separate time charges in this routine. Regardless of which of

the three alternatives (no link, retrieve link, pick link randomly)

dictates the results of Sll, a basic time increment representing the re-

trieval process is added. The time parameter which defines the increment

is the same as the one used by routine SlOl (which has a value of 10

milliseconds in runs to date). In other words, the basic retrieval process

is viewed as requiring the same amount of time regardless of whether

component or link information is being retrieved. If, however, the link

54

exists and is retrieved (the second alternative), an additionnl time charge

for updating the link is added. This time charge is the same as the charge

for the Update Routine, 552 (also 10 milliseconds to date).

Most of the basic processes in the model have now been described.

As one might imagine, the model continues the cycle of taking in a new

item (which includes setting up its component substructures and the link

substructure on the previous item) , sorting the new item through the dis-crimination net and updating it, and then rehearsing the items that have

already occurred, always starting with the first item in the sequence (the

item stored in Ml) . After taking in each new item and after rehearsingeach of the previous items, the window is checked. When another new item

occurs, the procedure starts over. This sequence of events (except forattempts to recode which are yet to be discussed) is continued until the new

item is the signal to respond. When the respond signal occurs control is

transferred to the Respond Routine, S6.

8. Responding

The Respond Routine is essentially the same as the Rehearsal Routine

except that an additional time charge is made after each item is retrievedfrom the net. The additional time charge represents the time it takes Sto actually output the item (say it aloud or write it on paper) . Thisrespond time charge is another time parameter in the model, and in the runs

to date a value of 500 milliseconds has been used.There is an additional characteristic of the Respond Routine that

might be mentioned. The Rehearsal Routine allows for a blank item to beoutput by the Net Sorting Routine, S4. The Respond Routine contains an

option for allowing or not allowing a blank. Computer runs where blanks

55

are not permitted, represent an experimental situation where j> knows how

many items were input and is required to output the same number (if he

does not remember an item, he must guess). Where blanks are allowed the

model is presumably simulating a situation where S can output as many

items (more or less than were input) as he chooses.

Since the Respond Routine is the last step in the Subject Executive

Routine Fig. 5, the completion of S6 also causes the SI routine to be

exited. Control is then transferred back to the Model Executive Routine,

El which may do several things. If all of the sequences have been

simulated for this run, the program may simply be terminated. If there

are additional sequences to be simulated, El resets the value of the

clock to zero, erases all of the information from the memory cells rendering

them empty, sets up the next sequence to be simulated, and again executes

the Subject Executive Routine.

9. Recoding

The one remaining part of the model that has not yet been discussed

is the Recoding Routine, SllO. The concept of recoding or chunking was

first introduced by Miller (1956). It refers to the process of combining

several items into a "larger unit" which can then be processed as a

single entity. Miller has shown that the memory span for items is greater

when the items are chunked. At the current stage of the model's development,

routine SllO has not been debugged completely, and in fact has not been

included in any of the simulation runs to be discussed in this paper.

Nevertheless, some of the basic ideas as to how the recoding process fits

into the model have been developed.

In considering the nature of the recoding process, it is immediately

56

obvious that some rule must exist for defining the chunk. While j>s

undoubtedly combine items into a chunk according to a great many rules,

two have been considered in the context of the present model. The first

rule is based upon meaningfulness. A meaningful chunk can be formed when

a string of items can be combined into a unit with which S is already

familiar. An obvious example is a string of letters that form a familiar

word. Another example is the sequence of digits 1492 which has meaning

to most Ss.

A second rule for defining a chunk in the model is based upon pro-

nounceability. A sequence of items can be combined into a single unit if

the string has a pronounceable name. For example, the sequence of lettersDUP can be recoded into a pronounceable chunk and processed as a single

unit. Note that words are consistent with both the pronounceability and

meaningfulness rules for recoding. Not all meaningful combinations, how-

ever, are readily formed into pronounceable chunks. Sequences such as

FBI and IBM illustrate this point.

The first effort to develop a chunking process in the model focuses

upon the pronounceability rule. That is, a set of procedures have been

spelled out that permit the model to recode strings of letters or digits

into a pronounceable chunk. This Recoding Routine, SllO, is executed by

the Interitem Activity Routine, Fig. 11, after all of the items presented

thus far have been rehearsed. Two pronounceability rules are employed

to define a recodeable sequence of items: First, any set of three digits

can be recoded into a pronounceable chunk; and second any set of three

letters where the first and third are consonants and the second is a

vowel (i.e., any nonsense syllable) can be recoded into a pronounceable

57

chunk .When the Recoding Routine is executed the first thing that happens

is that the items in the STM are retrieved one at a time starting with

the item in Ml. The retrieval process here is the same as in the Rehearsal

or Respond Routines; namely, the SlOl routine retrieves the remembered

components, the S4 routine sorts the components through the net and outputs

a vocabulary item, and the S5 routine updates the memory structure. When

the items in Ml, M2, and M3have been retrieved, the recoding routine

examines them to see if they satisfy either recoding rule (i.e., they

are all digits or they form a CVC) . Incidentally, after retrieving eachof these items the window is checked to see if a new item has yet appeared.

If a new item does appear, the recoding process is immediately interrupted,

and control reverts back to the S2 routine which will then process the new

item. If either rule 1 or 2 is satisfied by the string of three items,

the three items are recoded into a pronounceable unit. If neither rule

is satisfied (e.g., all three items were consonants) the Recoding Routine

moves ahead and picks up the item in M4. Now the items contained in M2,

M 3and M4are examined to determine if they can be recoded. In this

fashion the Recoding Routine continues to consider all combinations of

three items until it finds a recodeable set (at which point it goes ahead

and recodes the items into a chunk) , or until it has considered all of

the items presented thus far, or until a new item occurs in the window

and interrupts the process.

What does it mean in the model to recode a set of three items into

a chunk? A number of things happen. The model first goes to LTM for

58

each of the three items and retrieves a set of auditory components which

represents the contribution the item makes to the name of the new chunk.The reader may return to Fig. 3 and recall the remarks describing the

information in LTM. It was mentioned that a third sublist associated witheach item in LTM contains information about recoding. Figure 13 presentsan example of one of these sublists (for the letter A). Two types of

information are contained in the recoding sublist. The first is a symbolwhich indicates that the item is a digit, vowel or consonant; from this theRecoding Routine gets its information to determine if a sequence of threeitems is recodeable. The second type of information in the substructure isthe auditory components that this item contributes to the chunk.

To understand the value of this information it is necessary to observewhat the model is attempting to do. The Recoding Routine is collectinga set of auditory components for each of the three items which it will thenput together to form a set of auditory components that will describe thesound of the name of the new chunk. For example, if the sequence of itemsis DUP, the Recoding Routine goes to the recoding sublist for item D andretrieves those auditory components contributed by the letter D when itappears as the first letter in a chunk. Next, the Recoding Routine goesto the receding sublist for the letter U and retrieves the auditory com-ponents that the letter U contributes to the chunk when it is in thesecond position. Finally, it goes to the recoding sublist for P andretrieves the auditory components contributed by P when it is in thethird position. Note that vowels only contribute to forming new chunkswhen they are in the second position (a CVC) . Hence, the sublist for theletter Am Fig. 13 contains only information that concerns A' s contribution

59

LO

AUDITORY COMPONENTSP39

VISUAL COMPONENTSVSV 7V 8

RECODING INFORMATION

TYPE OF ITEMDIGIT, VOWEL OR CONSONANT

AUDITORY COMPONENTS CONTRIBUTED TO CHUNK

2nd POSITIONP25

Figure 13. Recoding Information in Long-term Memory

60

J

when it is in the second position. For consonants, this sublist is

broken into two parts, one containing information for when the consonant

is in the first position and another containing information for the third12position. The sublists for digits, on the other hand, contain information

regarding the auditory components contributed by the digit when it is in

any one of the three positions.

The specific set of auditory components that the Recoding Routine

gathers up for DUP is P4, P3O and Pi. This set of auditory components

defines the name of the new chunk. The question now is "What is done

with the chunk?" The answer is that several things occur. First, a new

structure in the LTM is established that represents this chunk. If this

is the first chunk formed from the sequence of items, it represents the

38th item in LTM. Unlike the other items in LTM which have three sub-

structures (visual, auditory and recoding information), the structure

representing the chunk has only an auditory substructure. Naturally

this substructure contains the names of the chunk's auditory components.

A second set of events concerns changes in the STM brought about by the

recoding process. Without going into detail, a memory structure repre-

senting the chunk is added to the location containing the memory structure

12The acoustic contribution to the chunk made by a consonant in the firstor third position may be a function of the vowel that appears in thesecond position. However, for this initial formulation of the recodingprocess such effects are being ignored.

*

61

for the first item in the chunk. For example, if DUP were the firstthree

items in the sequence, a memory structure for the new chunk is added to

the structure stored in Ml, which is where the information about D is

located. The chunking structure does not replace the structure for the

letter D, but instead becomes another part of the overall structure in Ml.

The details of how this structure is set up will not be presented here. It

is sufficient to note that the memory structure for the chunk contains

substructures for each of the auditory components which in turn contain the

name of the component, a time tag as to when it was stored, and a decay

function describing its rate of loss. In addition, this memory structure

for the chunk contains link information which connects it to the location

of the next item in the sequence following the last item of the chunk

(in this example, M4)

It should now be possible to see how the recoding process can bring

about an improvement in the overall performance on the task. When the

model returns to the memory structure at a later time to rehearse orto

retrieve the items for responding, it starts with Ml and attempts to

retrieve the chunk. It does this by retrieving the auditory components

of the chunk that are remembered, sorting them through the net and rec-

ognizing the chunk (which is now stored in the net structure representing

LTM), updating the components of the chunk and then going to the link

structure to find the location of the next item. If successful, it finds

M 4and proceeds in the usual

fashion,

make up the chunk is less than the sum

individual items, and since in dealing

memory locations as when the items are

Since the number of components that

of the components that make up the

with a chunk there is no search for

retrieved individually (routine Sll)

62

the time required to rehearse the chunk is considerably less than the

time required to rehearse, on an individual basis, the items that make

up the chunk. Thus, the existence of chunks adds considerably to the

efficiency of the overall processing. Of course, during the Respond

Routine it is necessary to decode the chunk into its three items. This

procedure has not been worked out in detail in the present version of the

model. It seems reasonable to propose a process where the auditory

components of this chunk are taken as input, the LTM scanned and items

retrieved that are consistent with these components. Such a procedure