## NPTEL Theory of Computation Week 6 Assignment Answers 2024

1. Consider the following languages

L_{1}={a^{n}b^{n}a^{m}∣n,m≥0}

L_{2}={a^{n}b^{m}a^{n}∣n,m≥0}

Which of the following languages is DCFL?

- L
_{1} - L
_{1}∩L_{2} - L
_{1}∪L_{2} - L
_{1}∩L_{2}

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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 L_{1} and L_{2} be two languages such that L_{1}⊆L_{2}. Consider the following statements.

S_{1}:If L_{1} is DCFL then L_{2} is also DCFL

S_{2}:If L_{2} is DCFL then L_{1} is also DCFL

S_{3}:Either both L_{1} and L_{2} are DCFL or neither L_{1} nor L_{2} is DCFL

Which of the following is correct?

- S
_{1}is true - S
_{2}is true - S
_{3}is true - None of S
_{1},S_{2},S_{3}is true

Answer :-

5. Let L_{1} be a context-free language, L_{2} be a DCFL. Which of the following is not true?

L_{1}∪L_{2} is necessarily context-free

L_{1}∪L_{2} is necessarily context-free

L_{1}⋅L_{2} is necessarily context-free

L_{1}∪L_{2} 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?

- {ww
^{R}∣w∈{0,1}∗ and w^{R}is the reverse of w} - {ww∣w∈{0,1}∗}
- {w∣w∈{0,1}∗ and w has equal number of 0’s and 1’s}
- {a
^{n}b^{n}c^{m}or a^{n}b^{m}c^{n}∣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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