# NPTEL Theory of Computation Week 7 Assignment Answers 2024

By Sanket

## NPTEL Theory of Computation Week 7 Assignment Answers 2024

1. The union of two decidable languages is

• context-free but not necessarily regular
• regular
• decidable but not necessarily context-free
• recognizable but not necessarily decidable
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2. Which of the following languages is not Turing-recognizable?

• {⟨R⟩∣R is an RE and L(R)=∅}
• {⟨M⟩∣M is a NFA and L(M)=∅}
• {⟨G⟩∣G is a CFG and L(G)=∅}
• {⟨M⟩∣M is a TM and L(M)=∅}
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3. Consider the language
L={⟨G1,G2⟩∣G1,G2 are CFGs and L(G1)=L(G2)}

Then L is

• regular.
• decidable but not regular.
• Turing recognizable but not decidable.
• not Turing recognizable.
`Answer :- `

4. The intersection of two Turing-recognizable languages is

• context-free but not necessarily regular
• regular
• decidable but not necessarily context-free
• recognizable but not necessarily decidable
`Answer :- `

5. What can we say about the following two languages?

ATM={⟨M,w⟩∣M is a TM that accepts the string w}
ETM={⟨M⟩∣M is a TM and L(M)=∅}

• ATM is Turing recognizable, ETM is Turing recognizable
• ATM is co-Turing recognizable, ETM is Turing recognizable
• ATM is Turing recognizable, ETM is co-Turing recognizable
• ATM is co-Turing recognizable, ETM is co-Turing recognizable
`Answer :- `

6. Consider the following languages
L1={⟨L⟩∣L is a regular language such that |L|=10}
L2={⟨L⟩∣L is a regular language such that |L| is infinity}

Which of the following statement is true?

• L1 and L2 both are undecidable
• L1 and L2 both are decidable
• L1 is decidable but L2 is undecidable
• L1 is undecidable but L2 is decidable
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7. Which of the following statements is false?

• Complement of a regular language is also regular
• Complement of a DCFL is also a DCFL
• Complement of a decidable language is also decidable
• Complement of a Turing-recognizable language is also Turing recognizable
`Answer :- `

8. Consider the language
L={⟨D1,D2⟩∣D1,D2 are DFAs and L(D1)=L(D2)}

Then L is

• regular.
• decidable but not regular.
• Turing recognizable but not decidable.
• not Turing recognizable.
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