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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 7 of 14

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Q61.
The language {a^m b^n C^(m+n) | m, n ≥ 1} is

a.

regular

b.

context-free but not regular

c.

context sensitive but not context free

d.

type-0 but not context sensitive

Discuss
Answer: (b).context-free but not regular
Q62.
Consider the following grammar G:

S → bS | aA | b
A → bA | aB
B → bB | aS | a

Let Na(w) and Nb(w) denote the number of a's and b's in a string w respectively. The language L(G) ⊆ {a, b}+ generated by G is

a.

{ w | Na(w) > 3Nb(w)}

b.

{ w | Nb(w) > 3Nb(w)}

c.

{ w | Na(w) = 3k, k ∈ {0, 1, 2, ...}}

d.

{ w | Nb(w) = 3k, k ∈ {0, 1, 2, ...}}

Discuss
Answer: (c).{ w | Na(w) = 3k, k ∈ {0, 1, 2, ...}}
Q63.
L1 is a recursively enumerable language over Σ. An algorithm A effectively enumerates its words as w1, w2, w3, ... Define another language L2 over Σ Union {#} as {wi # wj : wi, wj ∈ L1, i < j}. Here # is a new symbol. Consider the following assertions.

S1 : L1 is recursive implies L2 is recursive
S2 : L2 is recursive implies L1 is recursive

Which of the following statements is true ?

a.

Both S1 and S2 are true

b.

S1 is true but S2 is not necessarily true

c.

S2 is true but S1 is not necessarily true

d.

Neither is necessarily true

Discuss
Answer: (a).Both S1 and S2 are true
Q64.
Consider the languages L1 = and L2 = {a}. Which one of the following represents L1 L2* U L1*

a.

A

b.

B

c.

C

d.

D

Discuss
Answer: (a).A
Q65.
Consider the DFA given. Which of the following are FALSE?

1. Complement of L(A) is context-free.
2. L(A) = L((11*0+0)(0 + 1)*0*1*)
3. For the language accepted by A, A is the minimal DFA.
4. A accepts all strings over {0, 1} of length at least 2.

a.

1 and 3 only

b.

2 and 4 only

c.

2 and 3 only

d.

3 and 4 only

Discuss
Answer: (d).3 and 4 only
Q66.
What is the complement of the language accepted by the NFA shown below?

a.

A

b.

B

c.

C

d.

D

Discuss
Answer: (b).B
Q67.
Consider the set of strings on {0,1} in which, every substring of 3 symbols has at most two zeros. For example, 001110 and 011001 are in the language, but 100010 is not. All strings of length less than 3 are also in the language. A partially completed DFA that accepts this language is shown below.
Missing arcs in the DFA are

a.

A

b.

B

c.

C

d.

D

Discuss
Answer: (d).D
Q68.
A deterministic finite automation (DFA)D with alphabet {a,b} is given below. Which of the following finite state machines is a valid minimal DFA which accepts the same language as D?

a.

A

b.

B

c.

C

d.

D

Discuss
Answer: (a).A
Q69.
Given the following state table of an FSM with two states A and B, one input and one output.
If the initial state is A=0, B=0, what is the minimum length of an input string which will take the machine to the state A=0, B=1 with Output = 1?

a.

3

b.

4

c.

5

d.

6

Discuss
Answer: (a).3
Q70.
Given below are two finite state automata (→ indicates the start state and F indicates a final state)Which of the following represents the product automaton Z×Y?

a.

A

b.

B

c.

C

d.

D

Discuss
Answer: (a).A
Page 7 of 14

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