## NPTEL Theory of Computation Week 1 Assignment Answers 2024

1. Any NFA having n states can be converted to a DFA having at most (select the smallest possible value)

- 2
^{n} - 3
^{n} - 2
^{n} - n
^{2}

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2. Consider the language L={w∣the number of 1’s in w is divisible by 3} over the binary alphabet {0,1}. What is the minimum number of states required for a DFA that accepts L?

- 1
- 2
- 3
- 4

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3. What is the ϵ-closure of state q_{1} in the following NFA?

- {q0,q1,q2}
- {q0,q1,q2,q3}
- {q0,q1}
- {q1}

Answer :-

4. Which of the following strings is accepted by the DFA below?

- 01011101
- 00111100
- 10100011
- 11000010

Answer :-

5. Let L_{1} and L_{2} be two regular languages. What can we say about the language L={w_{1}w_{2}∣w_{1}∈L_{1},w_{2}∈L_{2}}?

- L may or may not be regular
- L is regular
- L is not regular
- L is accepted by some NFA but there is no DFA that can accept L

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6. What is the language accepted by the following NFA?

- {w∈{0,1}∗∣w ends with 0 and begins with 1}
- {w∈{0,1}∗∣w begins with 0 and ends with 1}
- {w∈{0,1}∗∣w ends with 0 or begins with 1}
- {w∈{0,1}∗∣w begins with 0 or ends with 1}

Answer :-

7. Consider the language

L={w∈{0,1}∗∣w begins with 00}

How many states will the minimal DFA for L have?

- 2
- 3
- 4
- 5

Answer :-

8. Consider the following DFA.

What is the language accepted by this DFA?

- {w∈{0,1}∗∣w has exactly one 1}
- {w∈{0,1}∗∣w ends with a 1}
- {w∈{0,1}∗∣w begins with a 1}
- {w∈{0,1}∗∣w consists of only 1’s}

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