## NPTEL Theory of Computation Week 3 Assignment Answers 2024

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2. Which states are equivalent in the following DFA?

- q0 and q1 only
- q1 and q2 only
- q0 and q2 only
- q0,q1 and q2

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3. Which of the following is a regular language?

- {0
^{m}1^{m}|m>0 is a natural number} - {0
^{m}1^{n}|m,n>0 are natural numbers} - {0
^{m}1^{m}|m≥0 is a natural number} - {0
^{m}1^{n}|m,n≥0 are natural numbers such that m≥n}

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4. Which of the following is not a regular language?

{0^{m}|m is a natural number}

{0^{2m}|m is a natural number}

{0^{3m+2}|m is a natural numberm≥n}

{0^{m}2|m is a natural number}

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5. Which of the following statements is not true?

- Any regular language satisfies the pumping lemma.
- Any language that does not satisfy the pumping lemma cannot be regular.
- Any language that satisfies the pumping lemma must be regular.
- A language that is not regular may also satisfy the pumping lemma.

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6. Which of the following languages is not regular?

- {0
^{n}∣n is prime} - {0
^{i}1^{j}∣i,j≥0} - Set of binary strings where every occurrence of 1 is followed by 0
- Set of binary strings such that the numbers represented by them in binary representation is divisible by 3

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7. How many states are there in the minmal DFA corresponding to the following DFA?

- 3
- 4
- 6
- 8

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8. How many final/accepting states are there in the minmal DFA corresponding to the following DFA?

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