NPTEL Theory of Computation Week 4 Assignment Answers 2024

By Sanket

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?

• 01
• 0+1
• (0+1)
• 0011
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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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