NPTEL Theory of Computation Week 4 Assignment Answers 2024

NPTEL Theory of Computation Week 4 Assignment Answers 2024

1. Consider the following context-free grammar:

                            S→S0S1∣S1S0∣ϵ

Which of the following is the language generated by this grammar?

• Set of all palindromes
• Set of all even numbers
• Set of all strings having either only 0’s or only 1’s
• Set of all strings having equal number of 0’s and 1’s

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2. Consider the following grammar

                     S⟶PQ∣ϵ

                     P⟶PP∣ϵ

                     Q⟶QQ∣ϵ

Which of the following regular expressions generates the same language as the given grammar?

• 0^∗1^∗
• 0^∗+1^∗
• (0+1)^∗
• 00^∗11^∗

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3. Consider the following grammar

                            S⟶0AB∣1BA∣ϵ

                            A⟶0A0∣1A1∣ϵ

                            B⟶0B1∣1B0∣ϵ

Which of the following strings does not belong to the language generated by this grammar?

• 0011010
• 0101001
• 1101000
• 1011001

Answer :- 

4. Consider the following DFA.

Answer :- 

5. Choose the CFG that generates the same language generated by the regular expression (bab)^∗.

• S⟶babS∣ϵ
• S⟶bS∣aS∣ϵ
• S⟶babS∣bab
• S⟶baS∣abS∣ϵ

Answer :- 

6. Which of the following context-free grammars is ambiguous?

• S⟶0S1∣ϵ
• S⟶0S1∣0∣1∣ϵ
• S⟶0S0∣1S1∣0∣1∣ϵ
• S⟶S0∣0∣1∣ϵ

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7. Let D be a DFA with n states that accepts the language L. Let G be the context-free grammar having the least number of non-terminals that generates L. The number of non-terminals in G is at most (select the smallest possible value)

• n
• 2n
• n²
• 2n

Answer :- 

8. Which of the following is the context free grammar that generates the set of all palindromes over the alphabet {0,1}?

• S⟶0S0∣1S1∣0∣1
• S⟶0S0∣1S1∣0∣1∣ϵ
• S⟶0S0∣1S1∣ϵ
• S⟶0S1∣1S0∣ϵ

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