## NPTEL Theory of Computation Week 4 Assignment Answers 2024

1. Consider the following context-free grammar:

` S→S0S1∣S1S0∣ϵ`

Which of the following is the language generated by this grammar?

- Set of all palindromes
- Set of all even numbers
- Set of all strings having either only 0’s or only 1’s
- Set of all strings having equal number of 0’s and 1’s

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2. Consider the following grammar

```
S⟶PQ∣ϵ
P⟶PP∣ϵ
Q⟶QQ∣ϵ
```

Which of the following regular expressions generates the same language as the given grammar?

- 0
^{∗}1^{∗} - 0
^{∗}+1^{∗} - (0+1)
^{∗} - 00
^{∗}11^{∗}

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3. Consider the following grammar

```
S⟶0AB∣1BA∣ϵ
A⟶0A0∣1A1∣ϵ
B⟶0B1∣1B0∣ϵ
```

Which of the following strings does not belong to the language generated by this grammar?

- 0011010
- 0101001
- 1101000
- 1011001

Answer :-

4. Consider the following DFA.

Answer :-

5. Choose the CFG that generates the same language generated by the regular expression (bab)^{∗}.

- S⟶babS∣ϵ
- S⟶bS∣aS∣ϵ
- S⟶babS∣bab
- S⟶baS∣abS∣ϵ

Answer :-

6. Which of the following context-free grammars is ambiguous?

- S⟶0S1∣ϵ
- S⟶0S1∣0∣1∣ϵ
- S⟶0S0∣1S1∣0∣1∣ϵ
- S⟶S0∣0∣1∣ϵ

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7. Let D be a DFA with n states that accepts the language L. Let G be the context-free grammar having the least number of non-terminals that generates L. The number of non-terminals in G is at most (select the smallest possible value)

- n
- 2n
- n
^{2} - 2n

Answer :-

8. Which of the following is the context free grammar that generates the set of all palindromes over the alphabet {0,1}?

- S⟶0S0∣1S1∣0∣1
- S⟶0S0∣1S1∣0∣1∣ϵ
- S⟶0S0∣1S1∣ϵ
- S⟶0S1∣1S0∣ϵ

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