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Welcome to the Theory of Computation(TOC) MCQs Page

Dive deep into the fascinating world of Theory of Computation(TOC) with our comprehensive set of Multiple-Choice Questions (MCQs). This page is dedicated to exploring the fundamental concepts and intricacies of Theory of Computation(TOC), a crucial aspect of GATE CSE Exam. In this section, you will encounter a diverse range of MCQs that cover various aspects of Theory of Computation(TOC), from the basic principles to advanced topics. Each question is thoughtfully crafted to challenge your knowledge and deepen your understanding of this critical subcategory within GATE CSE Exam.

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Theory of Computation(TOC) MCQs | Page 4 of 14

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Q31.
Consider the following two statements:

I. If all states of an NFA are accepting
states then the language accepted by
the NFA is Σ∗ .
II. There exists a regular language A such
that for all languages B, A ∩ B is regular.

Which one of the following is CORRECT?

a.

Only I is true

b.

Only II is true

c.

Both I and II are true

d.

Both I and II are false

Discuss
Answer: (b).Only II is true
Q32.
In the context-free grammar below, S is the start symbol, a and b are terminals, and ϵ denotes the empty string S → aSa | bSb | a | b | ϵ Which of the following strings is NOT generated by the grammar?

a.

aaaa

b.

baba

c.

abba

d.

babaaabab

Discuss
Answer: (b).baba
Q33.
Consider an ambiguous grammar G and its disambiguated version D. Let the language recognized by the two grammars be denoted by L(G) and L(D) respectively. Which one of the following is true ?

a.

L (D) ⊂ L (G)

b.

L (D) ⊃ L (G)

c.

L (D) = L (G)

d.

L (D) is empty

Discuss
Answer: (c).L (D) = L (G)
Q34.
Which of the following regular expressions describes the language over {0, 1} consisting of strings that contain exactly two 1's?

a.

(0 + 1) * 11(0 + 1) *

b.

0 * 110 *

c.

0 * 10 * 10 *

d.

(0 + 1) * 1(0 + 1) * 1 (0 + 1) *

Discuss
Answer: (c).0 * 10 * 10 *
Q35.
Let N be an NFA with n states and let M be the minimized DFA with m states recognizing the same language. Which of the following in NECESSARILY true?

a.

m ≤ 2^n

b.

n ≤ m

c.

M has one accept state

d.

m = 2^n

Discuss
Answer: (a).m ≤ 2^n
Q36.
Consider the following languages.

L1 = {a^i b^j c^k | i = j, k ≥ 1}
L1 = {a^i b^j | j = 2i, i ≥ 0}

Which of the following is true?

a.

L1 is not a CFL but L2 is

b.

L1 ∩ L2 = ∅ and L1 is non-regular

c.

L1 ∪ L2 is not a CFL but L2 is

d.

There is a 4-state PDA that accepts L1, but there is no DPDA that accepts L2

Discuss
Answer: (b).L1 ∩ L2 = ∅ and L1 is non-regular
Q37.
Which of the following languages is (are) non-regular?

L1 = {0^m1^n | 0 ≤ m ≤ n ≤ 10000}
L2 = {w | w reads the same forward and backward}
L3 = {w ∊ {0, 1} * | w contains an even number of 0's and an even number of 1's}

a.

L2 and L3 only

b.

L1 and L2 only

c.

L3 only

d.

L2 only

Discuss
Answer: (d).L2 only
Q38.
Which of the following intuitive definition is true about LR(1) Grammar.

a.

For a grammar to be LR(1) it is sufficient that a left-to-right shift reduce parser be able to recognize handles of right-sentential form when they appear on the stack

b.

For a grammar to be LR(1) it is sufficient that a left-to-right shift reduce parser be able to recognize handles of left-sentential form when they appear on the stack

c.

For a grammar to be LR(1) it is sufficient that a left-to-right shift reduce parser be able to recognize handles of left-sentential form or right-sentential form when they appear on the stack

d.

All of the above

Discuss
Answer: (a).For a grammar to be LR(1) it is sufficient that a left-to-right shift reduce parser be able to recognize handles of right-sentential form when they appear on the stack
Q39.
Consider the Following regular expressions

r1 = 1(0 + 1)*
r2 = 1(1 + 0)+
r3 = 11*0

What is the relation between the languages generated by the regular expressions above ?

a.

L (r1) ⊆ L (r2) and L(r1) ⊆ L(r3)

b.

L (r1) ⊇ L (r2) and L(r2) ⊇ L(r3)

c.

L (r1) ⊇ L (r2) and L(r2) ⊆ L(r3)

d.

L (r1) ⊇ L (r3) and L(r2) ⊆ L(r1)

Discuss
Answer: (b).L (r1) ⊇ L (r2) and L(r2) ⊇ L(r3)
Q40.
Consider regular expression r, where r = (11 + 111)* over Ʃ = {0, 1}. Number of states in minimal NFA and DFA respectively are:

a.

NFA – 3, DFA – 4

b.

NFA – 3, DFA – 3

c.

NFA – 3, DFA – 3

d.

NFA – 4, DFA – 4

Discuss
Answer: (a).NFA – 3, DFA – 4
Page 4 of 14

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