ISRO | ISRO CS 2017 | Question 23

Identify the language generated by the following grammar

S -> AB
 A -> aAb|ϵ
 B -> bB| b 

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


Answer: (D)

Explanation:

S -> AB
 A -> aAb|ϵ
 B -> bB| b 

strings generated by the the language:
b, bb, abb, abbb, aabbb and so on.

Alternative way –
The production rule B -> bB| b will generate b^p, p ≥ 1
The production rule A -> aAb|ϵ will generate a^mb^m, n ≥ 0
The production rule S -> AB will generate a^mb^(m+p), i.e.,

{ambn | n>m, m>=0}

So option (D) is correct.

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