# NPTEL Theory of Computation Week 6 Assignment Answers 2024

By Sanket

## NPTEL Theory of Computation Week 6 Assignment Answers 2024

1. Consider the following languages
L1={anbnam∣n,m≥0}
L2={anbman∣n,m≥0}

Which of the following languages is DCFL?

• L1
• L1∩L2
• L1∪L2
• L1∩L2
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2. Which of the following languages is not necessarily context-free?

• Complement of a DCFL
• Intersection of a DCFL and a regular language
• Union of two DCFLs
• Intersection of two DCFLs
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3. Which of the following languages is necessarily deterministic context-free?

• Complement of a DCFL
• Intersection of a DCFL and a regular language
• Union of two DCFLs
• Intersection of two DCFLs
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4. Let L1 and L2 be two languages such that L1⊆L2. Consider the following statements.
S1:If L1 is DCFL then L2 is also DCFL
S2:If L2 is DCFL then L1 is also DCFL
S3:Either both L1 and L2 are DCFL or neither L1 nor L2 is DCFL

Which of the following is correct?

• S1 is true
• S2 is true
• S3 is true
• None of S1,S2,S3 is true
`Answer :- `

5. Let L1 be a context-free language, L2 be a DCFL. Which of the following is not true?

L1∪L2 is necessarily context-free
L1∪L2 is necessarily context-free
L1⋅L2 is necessarily context-free
L1∪L2 is necessarily context-free

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6. Which of the following statements is not true about a deterministic Turing Machine?

• Equivalent to a nondeterministic Turing Machine in terms of computability
• Can go to multiple configurations from a given configuration
• Can have multiple accept configurations
• Accepts a decidable language
`Answer :- `

7. Which of the following is a deterministic context-free language?

• {wwR∣w∈{0,1}∗ and wR is the reverse of w}
• {ww∣w∈{0,1}∗}
• {w∣w∈{0,1}∗ and w has equal number of 0’s and 1’s}
• {anbncm or anbmcn∣m,n are natural numbers}
`Answer :- `

8. Which of the following statements is not true about a Turing Machine?

• Can move across the work tape in both directions
• Can write on the work tape
• Has a fixed (independent of the input) number of states
• Has a fixed (independent of the input) number of configurations
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