GATE | GATE CS 2010 | Question 40

Consider the languages – 
L1 = {0ⁱ1^j | i != j}. 
L2 = {0ⁱ1^j | i = j}. 
L3 = {0ⁱ1^j | i = 2j+1}. 
L4 = {0ⁱ1^j | i != 2j}.

(A)

Only L2 is context free

(B)

Only L2 and L3 are context free

(C)

Only L1 and L2 are context free

(D)

All are context free

Answer: (D)

Explanation:

 All these languages have valid CFGs that can derive them. 
 Hence, all of them are CFLs. 
 Intuitively, (A) & (B) are well known CFLs and CFGs for (C) & (D) could be made by little modifications in A & B’s CFGs.

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