Regular Expressions Questions

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21.

Which grammar is not regular

A

0^n

B

0^n 1^n n

C

0^m 0^n n

D

0^n 0^n n

Correct Answer: A

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22.

If is a language, and is a symbol, then, the quotient of and, is the set of strings such that is in: is in. Suppose is regular, which of the following statements is true?

A

L/a is always a regular language

B

L/a is not a regular language

C

Both of the mentioned

D

None of the mentioned

Correct Answer: A

L/a is always a regular language

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23.

Here is a context-free grammar G: S ? AB A ? 0A1 | 2 B ? 1B | 3A which of the following strings are in L (G)?

A

021300211

B

022111300211

C

None of the mentioned

D

Both of the mentioned

Correct Answer: D

Both of the mentioned

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24.

The grammar G: S ? SS | a | b is ambiguous. Check all and only the strings that have exactly two leftmost derivations in G

A

bbb

B

ab

C

All of the mentioned

D

None of the mentioned

Correct Answer: C

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25.

For the following grammar: S ? A | B | 2 A ? C0 | D B ? C1 | E C ? D | E | 3 D ? E0 | S E ? D1 | S Identify all the unit pairs

A

D,C

B

A,B

C

B,C

D

A,C

Correct Answer: A

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26.

The classes of languages P and NP are closed under certain operations, and not closed under others. Decide whether P and NP are closed under each of the following operations.
1. Union

2. Intersection

3. Intersection with a regular language

4. Kleene closure (star)

5. Homomorphism

A

Inverse homomorphisma) P is not closed under union

B

NP is not closed under intersection.

C

None of the mentioned

D

Both of the mentioned

Correct Answer: D

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27.

Consider the languages L1 = and L2 = {a}. Which one of the following represents L1 L2* U L1*

B

a*

C

All of the mentioned

D

None of the mentioned

Correct Answer: A

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28.

Given the language L = {ab, aa, baa}, which of the following strings are in L*?
1) abaabaaabaa

2) aaaabaaaa

3) baaaaabaaaab

4) baaaaabaa

A

1, 2, 3

B

2, 3, 4

C

1, 2, 4

D

1, 3, 4

Correct Answer: C

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29.

Given the language L = {ab, aa, baa}, which of the following strings are in L*?
1) abaabaaabaa

2) aaaabaaaa

3) baaaaabaaaab

4) baaaaabaa

A

1, 2, 3

B

2, 3, 4

C

1, 2, 4

D

1, 3, 4

Correct Answer: C

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30.

Which of the following are regular sets?
I. { a^n b^2m | n>=0, m>=0}

II. {a^n b^m |n=2m}

III. {a^n b^m | n!= m}

IV {xcy |x,y

A

I and IV

B

I and III

C

I and only

D

IV

Correct Answer: A

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