The GRE Advanced Test in Computer Science*

The

GRE

Advanced

Test in

Computer

Science*

Richard

H.

Austing

University

of

Maryland

Introduction

The

Graduate

Record

Examination,

for

many years an

aid to

graduate

schools

in

the

student

admission

and

placement process, was

augmented

last

year to include

an

advanced computer

science test.

Culminating

a

4-year

development

effort, the new test was

administered

for

the

first time on

October 16, 1976. Design of the overall

scope and

content

of

the test was carried

out

by a

"Committee

of

Examiners," appointed

in

1972

by the

GRE

Board.' Beginning

in

1977, the

Advanced

Computer

Science Test will be

annually

updated by the

Committee

of

Examiners

and

administered

five times per year as a

regular part of the GRE

Program.

Testing

has been the major

vehicle for the GRE

Program. Two types of

examinations

are offered: an

aptitude

test,

consisting

of

two

parts, verbal and

quanti-tative;

and advanced

tests

in

20

disciplines

(now

including

computer

science). These are

administered

on

specified

dates

at GRE test

centers in

the

United

States and other

countries,

and at

other times and places by

special

arrangement.

Score'

reports are sent

to

the

institutions

designated

by candidates

taking the tests, and

to

the

candidates themselves.

Scores on the test are

intended

to indicate

studehts'

abilities and mastery of the

subject

matter

emphasized

in

many

undergraduate

programs. Since past

achieve-ment is usually a good

indicator

of

future

performance,

such

scores can aid in

predicting

success in advanced

study.

A

standardized

test

also allows

comparison of

the

performance

of

students

from

different institutions

with

different programs

on a

single

measure

of

competence

in the

field. Test scores are

intended

for use pnly in

conjunction

with other

measures of

competence,

such as

prior

academic grades, letters of

recommendation,

and

previous experience,

in

evaluating students

for

graduate

admission.

They are not intended for use in other

evalua-tions.

Development

of

the

test

In

determining

the

scope of the test, the

committee

considered

tentative content

specifications

which had

*A

fullerversionofthispaperappearedin theSeptember1977 issue of

Communications of the

4ss

qciation

for,C7omputing

Machinery,

copy-righted bytheACM.

previously

been

sent to

degree-granting

departments.

A

revised version

(Appendix A)

was

agreed

upon

after

lengthy

discussion.

Various

factors influenced

the

choices

made in the

content

specifications,

the

most

significant

of

which

are

the

following:

(1)

Since

undergraduate

computer

science curricula

still vary

a

great

deal from

one

institution

to

the

next,

the

content

focuses

on

material

which should be common

to

all

or

almost all such programs.

(2)

In

the

content

specifications,

and

specifically

in

the

examination

questions themselves,

an

attempt

was

made

to

define the spectrum of computer

science

subject

matter

broadly

rather than

narrowly.

(3)

The

committee's

belief

in

the centrality

of

pro-gramming

systems

and

methodology

to

the

discipline

of computer

science

is

reflected

in

the

emphasis

given

to

this

area

in

the

content

specifications.

(4)

The

"Computer Systems"

section

of the

specifica-tions

might

well

be more extensive were it not for the

fact

that other parts

of

the specifications

contain

aspects

of

this

area

(e.g., "Operating Systems" under

"Programming

Systems and

Methodology").

(5) "Theory

of

Computation"

is

given

a

relatively

small

portion

of

the total

at

least

in

part

because

of

the

wide variation

in

approach

to

this

area in

under-graduate

curricula.

(6)

The committee

believes

that any

undergraduate

curriculum

in

'computer

science should

contain a

sig-nificant component

of

computational

mathematics.

(7)

The

short

shrift

given

to

"Special Topics" reflects

not a

belief

that

they

are

of

little

importance,

but

rather the great variability

in

whether they are

covered

in

undergraduate

curricula. The

committee

expects

that

some

of

these

topics

will

"graduate"

into

other

portions

of

the

specifications

in

future years.

Test

questions

were

solicited from

a

large

number

of computer scientists.

Questions

received and

those

questions

supplied

by

the

committee were

reviewed.

Questions

were

categorized, using the

content

specifica-tionsas a

guide,

and then identified

according

to

approx-imate

degree

of

difficulty.

An

experimental

test

consisting

of 36

questions

was

prepared

and

was

administered

to 320

students

in

the

fall of

1975.

The

results

were

analyzed for effectiveness

and reliability by the

same

statistical

methods

used

on

all

advanced

tests in

other fields and

were

found

to

be

satisfactory.

The committee

then

selected questions ip proportions

to

match the

content

specifications and assembled

two tests, one

for October

1976

and the other for December

1976.

Plans

were

made

to

solicit additional questions

for

the

April

1977 test

and then for each

subsequent

test.

Sample questions, similar

to

those

in

the

tests, are

given

in

Appendix B. They

are

taken from the

previously

cited descriptive

booklet

on

the

Advanced

Test in

Computer Science,

but

the

content

distribution

in

this sample

does

not

match the

percentages

given

in

Appendix

A.

Summary

The GRE Advanced Computer Science

Test

will impact

undergraduate

programs in

colleges and universities

that

offer

baccalaureate

degrees

in computer

science.

It

will also

become

a

guideline, although

not

intended

for that

purpose,

for

course

and

curriculum

development

in

institutions

not now

providing

an

undergraduate

major

in

the

field.

Consequently,

it

is

imperative that

as many computer

scientists

as

possible.

contribute

to

the continuing development of the

test,

either

by

provid-ing

critical

comments to

the committee concerning

the

content

specifications

or

by writing questions for the

test. In

addition, educationally oriented

groups

within

profes-sional societies

are

welcome

to

provide questions,

com-ments, or

suggestions for future committee members.

Although there

are

constraints

on

the

amount

of

change

which

can occur

from

test to test,

broad-based

support

and

interest

from

concerned educators will

ensure

the

development

of

the Advanced

Computer Science

Test in away

that

is consistent

with

the

growth

of

the

discipline. U

Reference

1. "A

Description

of the Advanced Computer Science Test, 1976-77," GRE, Educational Testing Service, Princeton, NJ 08540.

Appendix

A-Content

Specifications

for

the GRE

Advanced Computer

Science Test

The items included in parentheses are intended to be examplesoftopicsundertheheadingsand notexhaustive lists.

I. Programming Systems and Methodology (40%) A. Programming Languages and Their Processors

(evaluation of expressions, blockstructure,

parameterpassing and binding, control

struc-tures,assemblers, compilers,interpreters) B. Programming Concepts

(iteration, recursion, modularity, abstraction, refinemeiit,verification, documentation) C.

Propertips

ofAlgorithms

(timeandspacerequirementsofprograms, especially ofcommonprocessessuchassorting

andsearching;

correctnppp

ofprograms) D. DataStructures

(linear datastructures,liststructures,strings, stacks,queues,trees)

E. Operating Systems

(scheduling,

resource

and

storage

allocation,

interrupts,

synchronization,

addressing

techniques,

file

structures,

editors, batch/time

sharing,

networks/communications)

II. Computer

Systems

(20%)

A. Logic Design

(switching

algebra,

combinattorial

and

sequen-tial

networks)

B. Implementation of Computer Arithmetic

(codes, number representation,

add/subtract/

multiply/divide)

C. Processor

Organization

(instruction sets,

registers,

data andcontrol

flow, storage)

D. System Architecture

(configurations of and

communication among processors,

memories,

and I/O devices)

III. Theory of Computation (15%) A. Automata Theory

(sequential machines, transitions, regular

expressions, Turing machines, nondeterministic

finite

automata)

B. Analysis of

Algorithms'

(complexity of specific

al

qritms, exact/

asymptotic/lower

bound4'apiis,

anglysis

of

time/space complexity,

cojf

d"pess)

C. Formal

Languages

(regular and

context-free

grnars/laqipges,

simple properties such

as

pWiness or'

ambiguity)

IV. Computational

Mathematics

(20%)

A.

Discrete

Structures

(logic,

sets,

relations, functions,

Boolean

algebra, linear algebra, graph theory,

combina-torics)

B. Numerical Mathematics

(arithmetic,

number representation,

numpripl

algorithms,

error

analyIs, discrete

proba1bkil

elementary

statistics)

4 -z;

V.

Special Topics (5%)

(simulation and

modeling,

,ita

management systems,

information

retrieval,

artificial

intelili-gence)

Appendix

B-Sample

Questions

for

the

Advanced Test

in

Computer Science

The

following

questions

are

similar

to

those

in

the

test.

Because

of

space

limitations, however, it is

not

possible

to

include sufficient

examples

here

to

illustrate

the full

range

of the actual

testin terms

of

the

abilities measured,

the

subject-matter

areas

tested,

or

the

difficulty

of the

questions

posed.

An answer

key

appears at

the

end.

Notation and conventions. In this test a reading knowledge of Fortran and Algol-like language is assumed. The following notational conventions are used unless otherwise indicated. 1. Allnumbers areassumed to be written in decimal notation. 2. logxdenotes

log,0x.

3.

lxJ

denotes thegreatestintegerthat islessthanorequal to x. 4. [xldenotes theleast integerthat isgreater than orequal to x.

5. x,=

O(fln))

denotes"x,hasorder

O(f(n))"

and means that lim n is finite.

n f(n)

6. lIdenotes"there exists."

Vdenotes"For all." =*denotes "implies."

denotes"not."

V denotes"inclusive or." itdenotes"exclusive or."

Adenotes "and"; also,juxtaposition ofstatements denotes"and,"e.g.,PQdenotes "P and

Q."

7. IfAand Bdenote sets, then

AUBisthe set of all elements that are inA orin Bor in both, and

-AnB is the set of allelements that are in both A and B. Aisthe set of allelements not inAthatarein some

speci-fied universalset.

8. Ina string expression: Ifaand bdenote stringsorsets of strings, then

Adenotesanullstring;

abdenotes the concatenation ofaand b; a+bdenotes aUb or {a,b}dependingoncontext

andenotesaa...a;and nfactors

a*

denotesA+

a+a2+a3 +.... 9. Inagrammar,

a-'-fP

representsaproduction-inthe grammar.

a.f meansPcanbederived from aby theapplication of

exactlyoneproduction.

a means ( canbederived from a by the application of zero or moreproductions.

10. Inalogicdiagram,

D represents thelogical AND function D represents thelogical OR function

D' representsthelogical NAND function

>0

represents the logical NOT function D o representsthelogical NOR function

11. Binarytreetraversal isdefinedrecursivelyasfollows: preorder-visit the root, traverse the leftsubtree, traverse

theright subtree

inorder-traverse the left subtree, visit the root, traverse the

right

subtree

postorder-traverse the left subtree, traverse the right

subtree,

visit theroot

Directions. Each of the questions or incomplete statements below is followed by five suggested answers or completions.

In each case, select the one answer which is the best of the choices offered and then blacken the corresponding space on theanswersheet.

1. Which of thefollowingistrueofinterrupts?

(A) Theyaregenerated when memory cyclesare"stolen."

(B) Theyareused inplaceofdatachannels.

(C) Theycan indicatecompletion ofan I/O operation. (D) They cannot be generated by arithmetic operations.

(E)

None of the above.

Questions2and3 arebasedonthefollowinggrammar. A-RBC

B-xlBx

C-BID

D-ylEy

Em z December 1977

2. The nonterminal

alphabet

ofthe grammar is

(A)

{A,B,C,D,E}

(B) {B,C,D,E}

(C)

{A,B,C,D,E,x,y,zJ

(D) {x,y,z} (E) {z}

3. Which of the

following

is NOTasentencethat is

generated

by

the

grammar?

(A)

xy

(B)

xxzy (C) xyz

(D)

xxxxy

(E)

xxx Decimal

Binary

Digit

Encoding

0 11000 __ 1 00011 2 00101 __ 3 00110 4 01001 5 01010 6 01100 7 10001 8 10010 9 10100

4. Thetable abovesummarizesacodingschemefor

represent-ing

thedecimal

digits

0-9. Which of the following state-mentsabout thecode is true?

(A)

It is

weighted.

(B) It iserrorcorrecting.

(C)

It is

cyclic.

(D) It isexcess-two.

(E) None of the above

5. The

following

graph represents a finite state

machine,

where

SOistheinitial (start) state,

S3is the finalstate,

thearcsrepresent statetransitions, andeach arc label indicatesan

input

symbolandanoutput

symbol.

0/0

1/1

I

{0,1}/2

Forexample,ifthe machine is instateSO and thecurrent input symbolisa1, then the machine outputs thesymbol

0andenters stateS,.

Which of the followingregular expressions describes the

set of strings recognized by the finite state machine?

(A) 10*1

(B) 10*1

(C) (0+1)* (D) 0*(0+1)*0*

(E) 10*11*

Questions 6 and 7 are based on the following information. A certain computer represents floating-point numbersby

excess-16 base-4 exponent. The floating-point format is illustratedbelow.

Exponent Mantissa

lllo101011

1011 11

111010101

6. Thedecimal value of the number shown above is (A) -0.0546875

(B) -0.5

(C) -2.

(D)

-3.5 (E) -14

7. Of thefollowing, which best approximates the magnitude of the greatest number that can be represented in the floating-point format above?

(A) 1018 (B) 3 X 103 (C) 4 X 109 (D) 4 X 1018 (E) 109 A B-C *'D

8. The functionbythe network above is (A) ABE+ EF+CDF _ (B) (E+

ABF)(C

+D+

F)

-(C) (AB+

EJ(E

+ F)(C +D+ F) (D) (A +B)E + EF +CDF (E) (A+B)E+EF +CDF 9. Let f(x)=ifx=1then0else[x*f(x-1)+x2] Thevalue of fl4)is

(A)

53 (B) 29 (C) 50 (D) 100 (E) 148

Questions 10and 11 arebasedon the

following

information. Arandom-access read/write semiconductor memory

chip

is organized into 128 words of 8 bits each. A block

diagramofthechipisshown below. DATAIN

,

CHIPSELECT ADDRESS 128WORDS X 8 BITS

C)

WRITE ENABLE

DATAOUT

10. Ignoring powersupply connections,the minimum number ofpin connections perchipis

(A) 23 (B) 25 (C) 26 (D) 138 (E) 146 132

11. Alarger memory of4Kwords of16bits each(K' = 1024) may be obtainedby connecting

(A) 32chipsin a16X 2array (B) 32 chips in a 32 X1array (C) 64chips in a 32 X 2 array (D) 64chipsin a8X8array

(E) 32chips in nospecialconfiguration

12. The balanced ternary number system isabase-3 system inwhich the threedigitsare0, 1, and-1(which is written as 1). The balanced ternary equivalent of the decimal number352/ is (A) 1111.01 (B) 1101.01 (C) 1101.11 (D) 1111.11 (E) 1101.11

13. Which of thefollowing statementsmustbe true? I.

Lxj

= rxl if and

only

ifxisan

integer.

II.

Lxj

+ 1=

rxl

if and

only

ifxisnotan

integer.

III.

Lxj [y]

=

rxl

yjfor allx,y. IV.

-Lxj

=

r-xl

for allx.

(A) IVonly (B) Iand IV only

(C) I, II, andIIIonly

(D) I, II, andIVonly (E) I, II, III, and IV 14. IfA={x,y,z}

B = {u,v,w,x}, and the universe is

{s,t,u,v,w,x,y,z},

then (AUB)n(AnB)= (A) {u,v,w,x}

(B)

{

I

(C) {u,v,w,x,y,z} (D) {u,v,w} (E) {u,v,w,y,z}

15. Thefollowingassemblylanguage program fragmentwas written forasingle-address computer withone accumula-torregister. LOAD MULT STORE ADD STORE MULT ADD-STORE B C TI A T2 T2 Ti z

Which arithmetic expression is implemented by the fragment? (A)

z8-t,

(bc -a) -t2 (B) z-(a+bc)2+bc (C) z- 2bc +a2 (D) z'-(a+bc) + bc (E) z-a+2bc

Questions16-18 arebasedonthefollowing programfragment:

(A) begin

(2) forI=1toN-1do

(3) forJ=I+ 1toNdo (4) ifA(i)<A(j) then

(5) begin

(6)

T=

A(J);

(7)

A(J)=A(I); (8) A(I)-T; (9) end (10) end

Assume thatthe program issyntacticallycorrect,that all variables are integer mode, that N has a value greater than 1,and that A isaone-dimensional array.

Upon entrytotheprogramfragment above,thevalue of N is6and the values of A(1). A(6)aregivenby:

A(1) A(2) A(3) A(4) A(5) A(6) -8

1

4 1 10

1-2

I-7

x3

16. After exit from the program fragment, the values of

A(1),...,A(6), respectively, will be

(A) 10,7,4,3,-2,-8 (B) 10, -8, 7, 4, 3,-2

(C) -8, -2,3, 4, 7,10

(D) 4, -8,-2,10,3,7

(E) -2,3,4, 7, -8,10

17. What is the maximum number of times intermsof N that the block from line(5)throughline (9)could beexecuted?

(A) N2 (B) Nlog2 N

(C) 1+2+3+....+N (D)

N(N

-1)

D) 2

(E) It cannot be determinedon thebasis of the infor-mation given.

18. If the order of statements (6), (7), (8) were changed to

(6') A(J)

=

A(i)

(7')

T=A(J);

(8') A(I)=T;

thentheresult of the program would be (A) unchanged forall A and N (B) independentof thevalues of A (C) changed for all values of N

(D) unchangedfor somevalues of AandN

(E) unpredictablefor some values of A and N 19. If x, yare stringvariables, A,Baresymbols,

N(x,y)=P(Ax,By) BQ(yB), P(x,y)=yAx,and

Q(x)

=

Ax,

then N(A,A) = (A) BAAABAAAB (B) BAAABBAAB (C) BAABAAAB (D) BAAAABAAB (E) BAAAABAAAB

20. Expressions in a certain language can be described in Backus-Naurform(BNF)asfollows:

<expression>::=

<term>I<expression>op1

<term> <term>::=<item> <term> op, <item>

<item>::=

<variable>j<number>

This syntax is most appropriate when theorderof evalua-tion is

(A) fromlefttorightalways

(B) fromlefttoright, butop, takes precedenceoverop2

(C) fromlefttoright,but

Opz

takesprecedenceoverop

(D) inanyorder,butop, takes precedenceoverOP2 (E) fromrighttoleftalways

21. Of thefollowing,which bestapproximates the ratio of the number ofnonterminalnodes in the total number of nodes inacomplete K-ary tree of depth N?

(A)-N

(B)

N-N-(C)

K 1 (D) K--_K

(E) log,0.

December1977

22. Inthefollowingprocedure

integerprocedure P(X,Y); integerX,Y; value x; begin

KE-5;L-8; P-x +y end

X is called by value and Y is called by name. If the procedure were invoked by the following program frag-ment

K-0;

Z-EP(K,L),

thenthe value Z would besetequalto

(A) 5

(B) 8

(C) 13

(D) 0

(E) noneof the above

Key 1. C 2. A 3. C 4. E 5. E 6. E 7. E 8. B 9. D 10. B 11. C 16. A 12. E 17. D 13. D 18. D 14. A 19. D 15. B 20. C 21. C 22. B

Richard H. Austing, chairman of the Com-mittee of Examiners that supervises the Advanced

Computer

Science Test, 'is an

associate

professor

in the

Department

of

Computer

Scienceatthe

University

of

Mary-land. He is

currently

involvedinthe adminis-tration of the educational program of the

department

in addition to

offering

courses

intheareasof file

processing,

datastructures, and computers and society. His activities in computer scienceeducation include chairmanship of ACM's Special Interest Group in Computer Science Education, a membership in ACM's Curriculum Committee in Computer Science, chairmanship of the Committee of Examiners for the GRE Advanced Test in Computer Science, and a membership inICCP's CertificationCouncil for the Certificate in Computer ProgrammingExamination. Austing holdsaPhDinmathematics fromtheCatholic University of America, anMSinmathematics from St. Louis University, andaBSinmathematicsfrom Xavier University.