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This book is provided FREE with test registration by the Graduate Record Examinations Board.Computer Science Test Practice Book This practice book contains 䡲 one actual full-length GRE C

This book is provided FREE with test registration by the Graduate Record Examinations Board.

Computer Science Test

Practice Book

This practice book contains

䡲 one actual full-length GRE Computer Science Test

䡲 test-taking strategies

Become familiar with

䡲 test structure and content

䡲 test instructions and answering procedures

Compare your practice test results with the performance of those who took the test at a GRE administration.

Visit GRE Online at www.gre.org

Listening.

Learning.

Leading.

Copyright © 2004 by Educational Testing Service All rights reserved.

EDUCATIONAL TESTING SERVICE, ETS, the ETS logos, GRADUATE RECORD EXAMINATIONS,

and GRE are registered trademarks of Educational Testing Service

The book contains important information about content specifications and scoring

COMPUTER SCIENCE TEST

PRACTICE BOOK

Table of Contents

Purpose of the GRE Subject Tests 3

Development of the Subject Tests 3

Content of the Computer Science Test 4

Preparing for a Subject Test 5

Test-Taking Strategies 6

What Your Scores Mean 6

Practice GRE Computer Science Test 9

Scoring Your Subject Test 47

Evaluating Your Performance 50

Answer Sheet 51

Purpose of the GRE

Subject Tests

The GRE Subject Tests are designed to help graduate

school admission committees and fellowship sponsors

assess the qualifications of applicants in specific fields

of study The tests also provide you with an assessment

of your own qualifications

Scores on the tests are intended to indicate

knowledge of the subject matter emphasized in

many undergraduate programs as preparation for

graduate study Because past achievement is usually

a good indicator of future performance, the scores

are helpful in predicting success in graduate study

Because the tests are standardized, the test scores

permit comparison of students from different

institutions with different undergraduate programs

For some Subject Tests, subscores are provided in

addition to the total score; these subscores indicate

the strengths and weaknesses of your preparation,

and they may help you plan future studies

Subject Tests be considered in conjunction with other relevant information about applicants Because numer-ous factors influence success in graduate school, reliance on a single measure to predict success is not advisable Other indicators of competence typically include undergraduate transcripts showing courses taken and grades earned, letters of recommendation, the GRE Writing Assessment score, and GRE General Test scores For information about the appropriate use

of GRE scores, write to GRE Program, Educational Testing Service, Mail Stop 57-L, Princeton, NJ 08541,

or visit our Web site at www.gre.org/codelst.html

Development of the Subject Tests

Each new edition of a Subject Test is developed by a committee of examiners composed of professors in the subject who are on undergraduate and graduate facul-ties in different types of institutions and in different regions of the United States and Canada In selecting members for each committee, the GRE Program seeks the advice of the appropriate professional associations

in the subject

The content and scope of each test are specified and reviewed periodically by the committee of examiners Test questions are written by the committee and by other faculty who are also subject-matter specialists and by subject-matter specialists at ETS All questions proposed for the test are reviewed by the committee and revised as necessary The accepted questions are assembled into a test in accordance with the content specifications developed by the committee to ensure adequate coverage of the various aspects of the field and, at the same time, to prevent overemphasis on any single topic The entire test is then reviewed and approved by the committee

4 COMPUTER SCIENCE TEST

PRACTICE BOOK

ETS staff assist the committee, providing information

and advice about methods of test construction and

helping to prepare the questions and assemble the test

In addition, each test question is reviewed to eliminate

language, symbols, or content considered potentially

offensive, inappropriate for major subgroups of the

test-taking population, or likely to perpetuate any negative

attitude that may be conveyed to these subgroups The

test as a whole is also reviewed to ensure that the test

questions, where applicable, include an appropriate

balance of people in different groups and different roles

Because of the diversity of undergraduate curricula,

it is not possible for a single test to cover all the

material you may have studied The examiners,

there-fore, select questions that test the basic knowledge and

skills most important for successful graduate study in

the particular field The committee keeps the test

up-to-date by regularly developing new editions and

revising existing editions In this way, the test content

changes steadily but gradually, much like most

cur-ricula In addition, curriculum surveys are conducted

periodically to ensure that the content of a test

reflects what is currently being taught in the

under-graduate curriculum

After a new edition of a Subject Test is first

admin-istered, examinees’ responses to each test question are

analyzed in a variety of ways to determine whether

each question functioned as expected These analyses

may reveal that a question is ambiguous, requires

knowledge beyond the scope of the test, or is

inappro-priate for the total group or a particular subgroup of

examinees taking the test Answers to such questions

are not used in computing scores

Following this analysis, the new test edition is

equated to an existing test edition In the equating

process, statistical methods are used to assess the

difficulty of the new test Then scores are adjusted so

that examinees who took a difficult edition of the test

are not penalized, and examinees who took an easier

edition of the test do not have an advantage

Varia-tions in the number of quesVaria-tions in the different

editions of the test are also taken into account in

this process

digit scaled scores with the third digit always zero.The maximum possible range for all Subject Test totalscores is from 200 to 990 The actual range of scores for

a particular Subject Test, however, may be smaller Themaximum possible range of Subject Test subscores is

20 to 99; however, the actual range of subscores forany test or test edition may be smaller than 20 to 99.Subject Test score interpretive information is provided

in Interpreting Your GRE Scores, which you will receive

with your GRE score report, and on the GRE Web site

The approximate distribution of questions in eachedition of the test according to content categories isindicated by the following outline The percentagesgiven are approximate; actual percentages will varyslightly from one edition of the test to another

I SOFTWARE SYSTEMS ANDMETHODOLOGY — 40%

A Data organization

1 Data types

2 Data structures and implementationtechniques

B Program control and structure

1 Iteration and recursion

2 Procedures, functions, methods, andexception handlers

3 Concurrency, communication, andsynchronization

C Programming languages and notation

1 Constructs for data organization andprogram control

2 Scope, binding, and parameterpassing

3 Expression evaluation

1 Compilers, interpreters, and run-time systems

2 Operating systems, including resource

management and protection/security

3 Networking, Internet, and distributed systems

4 Databases

5 System analysis and development tools

II COMPUTER ORGANIZATION AND

ARCHITECTURE — 15%

A Digital logic design

1 Implementation of combinational and

sequential circuits

2 Optimization and analysis

B Processors and control units

1 Instruction sets

2 Computer arithmetic and number representation

3 Register and ALU organization

4 Data paths and control sequencing

C Memories and their hierarchies

1 Performance, implementation, and management

2 Cache, main, and secondary storage

3 Virtual memory, paging, and segmentation

D Networking and communications

1 Interconnect structures (e.g., buses,

2 Parallel and distributed architectures

III THEORY AND MATHEMATICAL

BACKGROUND — 40%

A Algorithms and complexity

1 Exact and asymptotic analysis of specific

algorithms

2 Algorithmic design techniques (e.g., greedy,

dynamic programming, divide and conquer)

of specific problems

4 Computational complexity, including completeness

NP-B Automata and language theory

1 Models of computation (finite automata,Turing machines)

2 Formal languages and grammars (regularand context-free)

IV Other Topics — 5%

Example areas include numerical analysis, artificialintelligence, computer graphics, cryptography,security, and social issues

Note: Students are assumed to have a mathematical

background in the areas of calculus and linearalgebra as applied to computer science

Preparing for a Subject Test

GRE Subject Test questions are designed to measureskills and knowledge gained over a long period of time.Although you might increase your scores to someextent through preparation a few weeks or monthsbefore you take the test, last-minute cramming isunlikely to be of further help The following informa-tion may be helpful

A general review of your college courses isprobably the best preparation for the test How-ever, the test covers a broad range of subjectmatter, and no one is expected to be familiarwith the content of every question

▪

6 COMPUTER SCIENCE TEST

PRACTICE BOOK

the types of questions in the GRE Computer

Science Test, paying special attention to the

directions If you thoroughly understand the

directions before you take the test, you will have

more time during the test to focus on the

ques-tions themselves

Test-Taking Strategies

The questions in the practice test in this book

illus-trate the types of multiple-choice questions in the test

When you take the test, you will mark your answers on

a separate machine-scorable answer sheet Total

test-ing time is two hours and fifty minutes; there are no

separately timed sections Following are some general

test-taking strategies you may want to consider

䡲 Read the test directions carefully, and work as

rapidly as you can without being careless For

each question, choose the best answer from the

available options

䡲 All questions are of equal value; do not waste

time pondering individual questions you find

extremely difficult or unfamiliar

䡲 You may want to work through the test quite

rapidly, first answering only the questions about

which you feel confident, then going back and

answering questions that require more thought,

and concluding with the most difficult questions

if there is time

䡲 If you decide to change an answer, make sure you

completely erase it and fill in the oval

corre-sponding to your desired answer

䡲 Questions for which you mark no answer or more

than one answer are not counted in scoring

䡲 As a correction for haphazard guessing,

one-fourth of the number of questions you answer

incorrectly is subtracted from the number of

questions you answer correctly It is improbable

that mere guessing will improve your score

significantly; it may even lower your score

If, however, you are not certain of the correct

answer but have some knowledge of the question

answer choices, your chance of getting the rightanswer is improved, and it may be to your advan-tage to answer the question

䡲 Record all answers on your answer sheet Answersrecorded in your test book will not be counted

䡲 Do not wait until the last five minutes of atesting session to record answers on youranswer sheet

What Your Scores Mean

Your raw score–that is, the number of questions youanswered correctly minus one-fourth of the numberyou answered incorrectly–is converted to the scaledscore that is reported This conversion ensures that ascaled score reported for any edition of a Subject Test

is comparable to the same scaled score earned on anyother edition of the same test Thus, equal scaledscores on a particular Subject Test indicate essentiallyequal levels of performance regardless of the testedition taken Test scores should be compared onlywith other scores on the same Subject Test (Forexample, a 680 on the Computer Science Test is notequivalent to a 680 on the Mathematics Test.)Before taking the test, you may find it useful toknow approximately what raw scores would be required

to obtain a certain scaled score Several factors ence the conversion of your raw score to your scaledscore, such as the difficulty of the test edition and thenumber of test questions included in the computation

influ-of your raw score Based on recent editions influ-of theComputer Science Test, the table on the next pagegives the range of raw scores associated with selectedscaled scores for three different test editions (Notethat when the number of scored questions for a giventest is greater than the number of possible scaled scores,

it is likely that two or more raw scores will convert tothe same scaled score.) The three test editions in thetable that follows were selected to reflect varyingdegrees of difficulty Examinees should note that futuretest editions may be somewhat more or less difficultthan the test editions illustrated in the table

COMPUTER SCIENCE TEST

PRACTICE BOOK

Earn Selected Scaled Scores on

Three Computer Science Test Editions

That Differ in Difficulty

Raw ScoresScaled Score Form A Form B Form C

Number of Questions Used to Compute Raw Score

*Raw Score = Number of correct answers minus one-fourth the

number of incorrect answers, rounded to the nearest integer

Examples of Ways to Earn a Scaled Score

of 700 on the Edition Labeled as “Form A”

Number ofQuestions Questions Questions Questions Used

Answered Answered Not to Compute

Raw Score Correctly Incorrectly Answered Raw Score

For a particular test edition, there are many ways to

earn the same raw score For example, on the edition

listed above as “Form A,” a raw score of 31 would earn

a scaled score of 700 Below are a few of the possible

ways in which a scaled score of 700 could be earned

8 COMPUTER SCIENCE TEST

PRACTICE BOOK

To become familiar with how the administration will be conducted at the test center, first remove the answer sheet (pages 51 and 52) Then go to the back cover of the test book (page 46) and follow the instructions for completing the identification areas of the answer sheet When you are ready to begin the test, note the time and begin marking your answers on the answer sheet.

Copyright © 2002, 2003 by Educational Testing Service All rights reserved.

GRE, GRADUATE RECORD EXAMINATIONS, ETS, EDUCATIONAL TESTING SERVICE

and the ETS logos are registered trademarks of Educational Testing Service

FORM GR0329

THIS TEST BOOK MUST NOT BE TAKEN FROM THE ROOM.

GRADUATE RECORD EXAMINATIONS®

Do not break the seal until you are told to do so.

The contents of this test are confidential.

Disclosure or reproduction of any portion

of it is prohibited.

COMPUTER SCIENCE TEST

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COMPUTER SCIENCE TEST Time—170 minutes

70 Questions

Notation, Conventions, and Definitions:

In this test a reading knowledge of modern programming languages is assumed The following notational conventions and definitions are used

1 All numbers are assumed to be written in decimal notation unless otherwise indicated

2 x denotes the greatest integer that is less than or equal to x

3 x denotes the least integer that is greater than or equal to x

4 g n ( ) = O f n ( ( )) denotes “ g n( ) has order at most f n( )” and means that there exist positive constants

C and N such that g n( ) £ Cf n( ) for all n > N

g n( ) = W( ( ))f n denotes “g n( ) has order at least f n( )” and for this test means that there exist positive

constants C and N such that g n( ) ≥ Cf n( ) for all n > N

g n( ) = Q( ( ))f n denotes “ g n( ) has the same order as f n( )” and means that there exist positive constants

C1, C2, and N such that C f n1 ( ) £ g n( ) £ C f n2 ( ) for all n > N

5 $ denotes “there exists.”

" denotes “for all.”

Æ denotes “implies;” … is also used to denote “implies;” and fiis also used to denote “implies.”

ÿ denotes “not”; “A” is also used as meaning “ÿ A.”

⁄ denotes “inclusive or”; + also denote “inclusive or,” e.g., P Q + can denote “ P or ” Q

≈ denotes “exclusive or.”

Ÿ denotes “and”; also, juxtaposition of statements can denote “and,” e.g., PQ can denote “P and Q.”

A boolean formula is satisfiable if it is true under some assignment of boolean values for its variables

A boolean formula is a tautology (or is valid) if it is true under all assignments of boolean values for its variables

6 ∆ denotes the empty set

If A and B denote sets, then:

A » is the set of all elements that are in A or in B or in both; B

A « is the set of all elements that are in both A and B; B

A is the set of all elements not in A that are in some specified universal set

A is the cardinality of A

7 In a string expression, if S and T denote strings or sets of strings, then:

An empty string is denoted by e or by L ;

ST denotes the concatenation of S and T ;

S + denotes S T » or { , }T S T , depending on context;

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8 In a grammar:

a Æ represents a production in the grammar b

a fi means b can be derived from a by the application of exactly one production b

a fi means b can be derived from a by the application of zero or more productions * b

Unless otherwise specified,

(i) symbols appearing on the left-hand side of productions are nonterminal symbols; the remaining

symbols are terminal symbols;

(ii) the leftmost symbol of the first production is the start symbol; and

(iii) the start symbol is permitted to appear on the right-hand side of productions

9 In a logic diagram:

10 represents a D-type flip-flop, which stores the value of its D input when clocked

11 Binary tree traversal is defined recursively as follows

Preorder: visit the root, traverse the left subtree, traverse the right subtree

Inorder: traverse the left subtree, visit the root, traverse the right subtree

Postorder: traverse the left subtree, traverse the right subtree, visit the root

12 In a finite automaton diagram, states are represented by circles, with final (or accepting) states indicated by two

concentric circles The start state is labeled “Start” An arc from state s to state t labeled a indicates a

transition from s to t on input a A label a b indicates that this transition produces an output b A label

a1, a2, , a k indicates that the transition is made on any of the inputs a1, a2, , a k

13 For a program segment S and predicates P and Q, to say that the triple P S Q{ } { } is partially correct means that

if P is true before initiation of S, then Q is true upon termination of S To say that P S Q{ } { } is totally correct

means that it is partially correct and S terminates for all inputs for which P is true

Given that P S Q { } { } is partially correct, a precondition is any assertion that implies P, and a postcondition is any assertion that is implied by Q

14 A loop invariant for a while statement

while B do S

is an assertion that is true each time the guard B is evaluated during execution of the while statement

11

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

comple-tions Select the one that is the best of the choices offered and then mark the corresponding space on the answer sheet

1 Suppose that a certain software product has a mean time between failures of 10,000 hours and has a mean time

to repair of 20 hours If the product is used by 100 customers, what is its availability?

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3 Which of the following algorithms has running time Q( )n2 in the worst case but Q(nlogn) on average?

(A) Bubblesort

(B) Mergesort

(C) Heapsort

(D) Quicksort

(E) Tournament sort

4 Which of the following is the name of the data structure in a compiler that is responsible for managing

information about variables and their attributes?

(A) Abstract Syntax Tree (AST)

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5 Consider the following pseudocode

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Questions 7-8 are based on binary tree T shown below

7 Which of the following represents a postorder traversal of T ?

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9 Which of the following statements about Ethernets is typically FALSE?

(A) Ethernets use circuit switching to send messages

(B) Ethernets use buses with multiple masters

(C) Ethernet protocols use a collision-detection method to ensure that messages are transmitted properly

(D) Networks connected by Ethernets are limited in length to a few hundred meters

(E) Packets sent on Ethernets are limited in size

10 A k-ary tree is a tree in which every node has at most k children In a k-ary tree with n nodes and height h, which of the following is an upper bound for the maximum number of leaves as a function of h, k, and n ?

(A) logk n (B) logk h (C)

11 Which of the following is (are) true about virtual memory systems that use pages?

I The virtual address space can be larger than the amount of physical memory

II Programs must be resident in main memory throughout their execution

III Pages correspond to semantic characteristics of the program

(A) I only (B) II only (C) I and II (D) I and III (E) II and III

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12 Let T n( ) be defined by T( )1 = and 7 T n( +1)= 3n+T n( ) for all integers n ≥ Which of the following 1

represents the order of growth of T n( ) as a function of n ?

(A) Q( )n (B) Q(nlogn) (C) Q( )n2 (D) Q(n2logn) (E) Q( )2n

13 One approach to handling fuzzy logic data might be to design a computer using ternary (base-3) logic so that

data could be stored as “true,” “false,” and “unknown.” If each ternary logic element is called a flit, how many flits are required to represent at least 256 different values?

(A) 4 (B) 5 (C) 6 (D) 7 (E) 8

14 Hash tables can contribute to an efficient average-case solution for all of the problems described below

EXCEPT:

(A) Counting distinct values: Given a set of n keys, determine the number of distinct key values

(B) Dynamic dictionary: Support the operations of insert, delete, and search in a dictionary

(C) Range search: Given values a and b, find all the records whose key value is in the range a b,

(D) Symbol table lookup: Given a program identifier, find its type and address

(E) Finding intersections: Given two sets of keys, find all key values in common to both sets

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15 An invariant for the loop below is “z* k = n

(A) To translate Web addresses to host names

(B) To determine the IP address of a given host name

(C) To determine the hardware address of a given host name

(D) To determine the hardware address of a given IP address

(E) To determine the appropriate route for a datagram

17 A certain pipelined RISC machine has 8 general-purpose registers R0, R1, , R7 and supports the following operations

ADD Rs1, Rs2, Rd Add Rs1 to Rs2 and put the sum in RdMUL Rs1, Rs2, Rd Multiply Rs1 by Rs2 and put the product in Rd

An operation normally takes one cycle; however, an operation takes two cycles if it produces a result required

by the immediately following operation in an operation sequence Consider the expression AB + ABC + BC,

where variables A, B, C are located in registers R0, R1, R2 If the contents of these three registers must not

be modified, what is the minimum number of clock cycles required for an operation sequence that computes the

value of AB + ABC + BC?

(A) 5 (B) 6 (C) 7 (D) 8 (E) 9

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18 Below is a precedence graph for a set of tasks to be executed on a parallel processing system S

Efficiency is defined as the ratio between the speedup and the number of processors (The speedup is defined as the ratio of the time taken to perform a set of tasks on a single processor to the time taken to perform the same set of tasks on a parallel processor.)

System S has four processors (CPU’s) If each of the tasks T1, ,T8 takes the same time, what is the efficiency

of this precedence graph on S ?

(A) 25% (B) 331

3% (C) 50% (D) 100% (E) 125%

19 Let G = (V E, ) be a finite directed acyclic graph with E > Which of the following must be true? 0

I G has a vertex with no incoming edge

II G has a vertex with no outgoing edge

III G has an isolated vertex, that is, one with neither an incoming edge nor an outgoing edge.

(A) I only (B) II only (C) III only (D) I and II only (E) I, II, and III

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Questions 20-21 are based on the following information

Array A contains 256 elements of 4 bytes each Its first element is stored at physical address 4,096

Array B contains 512 elements of 4 bytes each Its first element is stored at physical address 8,192

Assume that only arrays A and B can be cached in an initially empty, physically addressed, physically tagged, direct-mapped, 2K-byte cache with an 8-byte block size The following loop is then executed

for (i = 0; i < 256; i++)

A[i] = A[i] + B[2*i];

20 During the execution of the loop, how many bytes will be written to memory if the cache has a write-through policy?

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22 According to the IEEE standard, a 32-bit, single-precision, floating-point number N is defined to be

N = (−1)S × 1.F × 2 E−127

where S is the sign bit, F the fractional mantissa, and E the biased exponent

A floating-point number is stored as S E F: : , where S, E, and F are stored in 1 bit, 8 bits, and 23 bits,

respectively What is the decimal value of the floating-point number C1E00000 (hexadecimal notation) ?

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Questions 24-25 are based on the following procedures

The output of procedure mystery depends on the parameter-passing method used

24 Suppose that all parameters are passed by value Which of the following values are output when procedure mystery is called?

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26 Let A and B be two sets of words (strings) from S*, for some alphabet of symbols S Suppose that B is a

subset of A Which of the following statements must always be true of A and B ?

I If A is finite, then B is finite

II If A is regular, then B is regular

III If A is context-free, then B is context-free

(A) I only (B) II only (C) III only (D) I and II only (E) I, II, and III

27 A CPU has an arithmetic unit that adds bytes and then sets its V, C, and Z flag bits as follows The V-bit is set if arithmetic overflow occurs (in two’s complement arithmetic) The C-bit is set if a carry-out is generated from the most significant bit during an operation The Z-bit is set if the result is zero What are the values of the V, C, and

Z flag bits after the 8-bit bytes 1100 1100 and 1000 1111 are added?

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28 Let k be an integer greater than 1 Which of the following represents the order of growth of the expression

(A) Q( )k n (B) Q(k nlogn) (C) Q(k nlogn) (D) Q( )k 2kn (E) Q( )n k+1

29 Mergesort works by splitting a list of n numbers in half, sorting each half recursively, and merging

the two halves Which of the following data structures will allow mergesort to work in O n( logn) time?

I A singly linked list

II A doubly linked list

III An array

(A) None (B) III only (C) I and II only (D) II and III only (E) I, II, and III

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30 Consider the following function

double power(double base, unsigned int exponent)

I Datagrams at the source must be the size of the smallest maximum transmission unit (MTU) of all the

links on a path to the destination

II Datagrams may be fragmented during routing

III Datagrams are reassembled only at the destination

(A) I only (B) II only (C) III only (D) I and III (E) II and III

25

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32 Of the following problems concerning a given undirected graph G, which is currently known to be solvable in

polynomial time?

(A) Finding a longest simple cycle in G

(B) Finding a shortest cycle in G

(C) Finding ALL spanning trees of G

(D) Finding a largest clique in G

(E) Finding a node coloring of G (where adjacent nodes receive distinct colors)

with the minimum number of colors

33 Two processors, M-5 and M-7, implement the same instruction set Processor M-5 uses a 5-stage pipeline and a clock cycle of 10 nanoseconds Processor M-7 uses a 7-stage pipeline and a clock cycle of 7.5 nanoseconds Which of the following is (are) true?

I M-7’s pipeline has better maximum throughput than M-5’s pipeline

II The latency of a single instruction is shorter on M-7’s pipeline than on M-5’s pipeline

III Programs executing on M-7 will always run faster than programs executing on M-5

(A) I only (B) II only (C) I and III only (D) II and III only (E) I, II, and III

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