NPTEL Theory of Computation Week 5 Assignment Answers 2024

NPTEL Theory of Computation Week 5 Assignment Answers 2024

1. Let L be a context-free language. Then according to the pumping lemma for context-free languages, there exists an integer p≥1 such that every string w∈L can be written as w=uvwxy satisfying the following conditions:

• ∣vx∣≥1
• ∣vwx∣≤pand

• ∀n≥0,uvⁿwxⁿy∈L
• ∃n≥0,uvⁿwxⁿy∈L
• ∀n≥0,uvⁿwxyⁿ∈L
• ∃n≥0,uvⁿwⁿxⁿy∈L

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2. Which of the following languages is not context-free?

• {}
• {aⁿbⁿw∣m,n≥0,w∈{0,1}∗}
• {aⁿbⁿc^md^m∣m,n≥0}
• {ww∣w∈{0,1}∗}

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3. Consider the following PDA.

What is the language accepted by this PDA?

• Set of all strings of the form aⁿbⁿ
• Set of all strings of the form bⁿaⁿ
• Set of all even-length palindromes over the alphabet {0,1}
• Set of all odd-length palindromes over the alphabet {0,1}

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4. Consider the following PDA.

Which of the following strings is not accepted by this PDA?

• 00000000
• 00000011
• 00001111
• 00111111

Answer :- 

5. Which of the following is context-free?

• {0ⁿ∣n is prime }
• {ww^R∣w∈{0,1}∗ and w^R is the reverse of w}
• {aⁿc^mbⁿd^m∣m,n≥0}
• {aⁿbⁿcⁿ∣n≥0}

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