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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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Check out the MCQs below to embark on an enriching journey through Theory of Computation(TOC). Test your knowledge, expand your horizons, and solidify your grasp on this vital area of GATE CSE Exam.

Note: Each MCQ comes with multiple answer choices. Select the most appropriate option and test your understanding of Theory of Computation(TOC). You can click on an option to test your knowledge before viewing the solution for a MCQ. Happy learning!

Theory of Computation(TOC) MCQs | Page 3 of 14

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Q21.
The number of states in the minimal deterministic finite automaton corresponding to the regular expression (0 + 1)*(10) is ____________

a.

2

b.

3

c.

4

d.

5

Discuss
Answer: (b).3
Q22.
Let T be the language represented by the regular expression Σ∗0011Σ∗ where Σ = {0, 1}. What is the minimum number of states in a DFA that recognizes L' (complement of L)?

a.

4

b.

5

c.

6

d.

8

Discuss
Answer: (b).5
Q23.
Which one of the following regular expressions is NOT equivalent to the regular expression (a + b + c) *?

a.

(a* + b* + c*)*

b.

(a*b*c*)*

c.

((ab)* + c*)*

d.

(a*b* + c*)*

Discuss
Answer: (c).((ab)* + c*)*
Q24.
Let L be a regular language and M be a context-free language, both over the alphabet Σ. Let Lc and Mc denote the complements of L and M respectively. Which of the following statements about the language Lc∪ Mc is TRUE?

a.

It is necessarily regular but not necessarily context-free

b.

It is necessarily context-free

c.

It is necessarily non-regular

d.

None of the above

Discuss
Answer: (d).None of the above
Q25.
Which of the following statements is TRUE about the regular expression 01*0?

a.

It represents a finite set of finite strings

b.

It represents an infinite set of finite strings

c.

It represents a finite set of infinite strings

d.

It represents an infinite set of infinite strings

Discuss
Answer: (b).It represents an infinite set of finite strings
Q26.
The language {0^n 1^n 2^n | 1 ≤ n ≤ 10^6} is

a.

regular

b.

context-free but not regular

c.

context-free but its complement is not context-free

d.

not context-free

Discuss
Answer: (a).regular
Q27.
A language L satisfies the Pumping Lemma for regular languages, and also the Pumping Lemma for context-free languages. Which of the following statements about L is TRUE?

a.

L is necessarily a regular language

b.

L is necessarily a context-free language, but not necessarily a regular language

c.

L is necessarily a non-regular language

d.

None of the above

Discuss
Answer: (d).None of the above
Q28.
Consider the context-free grammar E → E + E E → (E * E) E → id
where E is the starting symbol, the set of terminals is {id, (,+,),*}, and the set of nonterminals is {E}.
Which of the following terminal strings has more than one parse tree when parsed according to the above grammar?

a.

id + id + id + id

b.

id + (id* (id * id))

c.

(id* (id * id)) + id

d.

((id * id + id) * id)

Discuss
Answer: (a).id + id + id + id
Q29.
Consider the context-free grammar E → E + E E → (E * E) E → id
where E is the starting symbol, the set of terminals is {id, (,+,),*}, and the set of non-terminals is {E}.
For the terminal string id + id + id + id, how many parse trees are possible?

a.

5

b.

4

c.

3

d.

2

Discuss
Answer: (a).5
Q30.
The number of states in the minimum sized DFA that accepts the language defined by the regular expression (0+1)*(0+1)(0+1)* is __________________ .

a.

2

b.

3

c.

4

d.

5

Discuss
Answer: (a).2
Page 3 of 14

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