GATE | GATE-CS-2017 (Set 2) | Question 26

Identity the language generated by following grammar where S is the start variable.

S --> XY
X --> aX | a
Y --> aYb | ∈

(A) {a^m bⁿ| m>=n, n>0 }
(B) {a^m bⁿ| m>=n, n>=0 }
(C) {a^m bⁿ| m>n, n>=0 }
(D) {a^m bⁿ| m>n, n>0 }

Answer: (C)
Explanation:

S --> XY
X --> aX | a  // This produces only "a"
Y --> aYb | ∈  // This produces and "a" for every "b"                     

Option (A) and (B) are wrong because n can be zero also
due to epsilon in Y

Option (D) is wrong because Y–>aYb produces equal number of a’s and b’s.
Since there is one variable X which produces at least one a.
Therefore numbers of a’s are always greater than numbers of b’s.
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