NPTEL Theory of Computation Week 1 Assignment Answers 2024

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)

• 2ⁿ
• 3ⁿ
• 2ⁿ
• n²

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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 q₁ 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 L₁ and L₂ be two regular languages. What can we say about the language L={w₁w₂∣w₁∈L₁,w₂∈L₂}?

• 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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