UGC-NET | UGC NET CS 2014 Dec – II | Question 35

The following Context-Free Grammar (CFG): S → aB | bA A → a | aS | bAA B → b | bS | aBB will generate (1) odd numbers of a’s and odd numbers of b’s (2) even numbers of a’s and even numbers of b’s (3) equal numbers of a’s and b’s (4) different numbers of a’s and b’s

(A)

(1)

(B)

(2) an (3)

(C)

(1), (2) and (3)

(D)

All are correct.

Answer: (C)
Explanation:

Explanation: The following Context-Free Grammar (CFG): S → aB | bA A → a | aS | bAA B → b | bS | aBB will generate

• odd numbers of a’s and odd numbers of b’s i.e. ab or ba.
• even numbers of a’s and even numbers of b’s i.e. aabb or bbaa
• equal numbers of a’s and b’s i.e.ab, ba bbaa or aabb
• The grammar cannot produce variable numbers of a’s and b’s. i.e. abb or baa

Option (C) is correct.

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