ISRO | ISRO CS 2017 | Question 26

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 automata 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.

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