SCSJ3203 - Theory Science Computer - Midterm Paper - Universiti Teknologi Malaysia - UTM

1. UNIVERSITY TEKNOLOGI MALAYSIA
MIDTERM TEST
SEMESTER I 2013/2014
CODE OF SUBJECT
: SCSJ3203
NAME OF SUBJECT
: Theory of Computer Science
YEAR/COURSE
: 3SCSJ, 3SCSR, 3SCSV, 3SCSI, 3SCSD, 3SCSB
TIME
: 10.15 am – 12.15 pm (2 hours)
DATE
: 31 October 2013
VANUE
: BK1 – BK6 (N28)
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INSTRUCTION TO THE STUDENTS
PART A
PART B
: 10 TRUE/FALSE QUESTIONS (10 MARKS)
: 10 SUBJECTIVE QUESTIONS (90 MARKS)
THIS PAPER CONSIST OF 2 PARTS. ANSWER ALL QUESTION IN THE SPACE PROVIDED IN THIS QUESTION
PAPER. THE MARKS FOR EACH QUESTION IS AS INDICATED.
ANSWER ALL QUESTION IN THE SPACES ALLOCATED IN THIS BOOKLET.
Name
IC (or matric) number
Name of lecturer
Subject code and section
SCJ3203 Section 01 / 02 / 03 / 04 / 05 / 06
(pls. circle tour section)
This examination book consists of 6 printed pages excluding this page.

2. Part A – True and false questions
[10 marks]
_____________________________________________________________________________________
There are 10 questions in this section. For each question, state whether it is TRUE or FALSE and write your
answer in the space given. Each question carries 1 marks.
Answer
1.
λ is always subset of every set.
___________
2.
L1L2 = {xy | x ϵ L1 and y ϵ L2}, if L1 = {a, aa} and L2 = {λ, b, ab},
thus L1L2 = {a, b, aa, ab, aab, aaab}.
___________
3.
A regular expression for set of strings over {a, b} containing
two or more b’s is (a + b)*b(a + b)*b(a + b).
___________
4.
Two example expressions that represent the same set of
strings are (0 + 1 + λ)* and (0 + 1)*.
___________
5.
R = a* + b* generates any string with the combination of a’s
and b’s.
___________
6.
The following grammar; S → aS; S → baSS; S → b over
alphabet {a, b} is regular.
___________
7.
abab is generated by S → aX; X → bX; X → a;
___________
8.
A regular grammar does not generate the empty string.
___________
9.
A regular grammar is also a context-free grammar.
___________
10.
The following grammar; S → aX; X → bY; Y → aS; X → b;
generates the language of (aba)*ab.
___________
1

3. PART B – SUBJECTIVE QUESTIONS
[90 MARKS]
_____________________________________________________________________________________
This part consists of 10 structured questions. Answer all questions in the space provided. The marks for
each part of the question is as indicated.
1. Consider the language S* where S = {a, ab, ba}. Write three strings that are IN and NOT IN the
language in Table 1.
[6 marks]
Table 1
IN the language
NOT IN the language
2. For the two regular expression:
[4 marks]
r1 = a* + b*
r2 = ab* + ba* + b*a + (a*b)*
a. Find two strings corresponding to r2 but not r1.
b. Find two strings corresponding to both r1 and r2.
_____________________
_____________________
3. Find a regular expression corresponding to the following languages.
a. The language of all strings over the alphabet {a, b} that do not end with ba.
[4 marks]
___________________________________________________________________
b. The language of all strings over the alphabet {a, b} that contain no more than one
occurrence of the string bb.
[4 marks]
___________________________________________________________________
c. The language of strings of even lengths over the alphabet of {a, b}.
[4 marks]
___________________________________________________________________
2

4. 4. Describe as simply as possible in English the language corresponding to the following regular
expressions
a. (b + aa)(a + b)*
[3 marks]
_________________________________________________________________
_________________________________________________________________
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b. a*b(a*ba*b)*a*
[3 marks]
_________________________________________________________________
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5. construct a context-free grammar that generate the following language
a. {anbm | n<m}
[4 marks]
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b. {a3nb2n | n ≥ 0}
[4 marks]
____________________________________________________________________
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c. {a3n+1b2n | n ≥ 0}
[4 marks]
____________________________________________________________________
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____________________________________________________________________
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3

5. 6. For each of the following context-free grammar, write the equivalent regular grammar and regular
expression.
[18 marks]
Context free grammar
Regular grammar
Regular expression
S → aBa
B → bB | λ
S → abS | λ
S → Aa
A → aA | bA | λ
7. Design a CFG rules for the following regular expression.
[4 marks]
(a + b)*aa(a + b)*
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
8. Consider the following grammar
G1:
S → aSa | aBa
B → bB | b
a. Use the set notations to define the language generated by the grammar, L(G1).
[3 marks]
___________________________________________________________________________
b. What is the shortest string that can be produced from the grammar?
[1 mark]
___________________________________________________________________________
c. Write another possible string that can be generated from the language.
[1 mark]
___________________________________________________________________________
4

6. 9. Let G2 be the grammar
S → AB
A → aA | λ
B → bB | λ
a. Give a leftmost derivation of the string aabbb.
[3 marks]
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
b. Give the rightmost derivation of string abbbb.
[3 marks]
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
c. Build the derivation tree for the derivations in parts (a) and (b).
[4 marks]
5

7. d. Give a regular expression for L(G2). _________________________
[3 marks]
10. The following is a CFG to generate a language.
S → A1B
A → 0A | λ
B → 0B | 1B | λ
a. Give leftmost derivations of the following string.
[6 marks]
i. 00101
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____________________________________________________________________
____________________________________________________________________
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ii. 10001
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b. What is the regular expression for this CFG.
[4 marks]
___________________________________________________________________________
-END OF QUESTIONS6