Which of the following are context free?

A = {anbnambm | m, n>=0}
B = {ambnambn | m, n>=0}
C = {ambn | m≠2n,m, n>=0}

(A) A and B only
(B) A and C only
(C) B and C only
(D) C only


Answer: (B)

Explanation: First check for A :-
a^n & b^n and a^m & b^m must be comparable using one stack for CFL. Push all a^n into the stack then pop all b^n for each a^n if at the buttom of the having null the a and b both are equal similarly compare a^m and b^m can be compare as push a^m into the stack and pop b^m for each a^m , therefore it is context free language.

For B:-
This can not be done in to a single stack because m and n are not comparable we can not find when to push or when to pop so we need here more stack that’s why this is Context sensitive language.

For C:-
It is also Context free language because first make the autoamata for the language a^m b^n| m=2n then make final state as non final state and non final as final.

Option (B) is correct.

Quiz of this Question

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.