GATE | GATE CS Mock 2018 | Question 34

Consider the following context-free grammar over the alphabet ∑ = {a, b} with S as the start symbol:

S → AT 
A → aAa | bAb | #T 
T → aT | bT | λ 

Which of the following represents the language generated by the above grammar?
(A) { w#x | w^R is a substring of x, where w, x ∈ {a, b}* }
(B) { w#x | w is a substring of x, where w, x ∈ {a, b}* }
(C) { x#w | w^R is a substring of x, where w, x ∈ {a, b}* }
(D) { w#x | w, x ∈ {a, b}* }


Answer: (A)

Explanation: { w#x | w^R is a substring of x, where w, x ∈ {a, b}* }
The following grammar generates language L, where S is the start variable.

S → AT 
A → aAa | bAb | #T 
T → aT | bT | λ  

The strings in the language have the form w#uw^Rv, where u and v are strings of the form (a + b)* (any string made from symbols a and b). The variable T generates the strings u and v, while variable A generates the string w#uw^R and the variable S generates the desired string w#uw^Rv.



Option (A) is correct.

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