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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