GATE | GATE-CS-2015 (Set 3) | Question 42

Which of the following languages are context-free?

L1 = {ambnanbm ⎪ m, n ≥ 1}
L2 = {ambnambn ⎪ m, n ≥ 1}
L3 = {ambn ⎪ m = 2n + 1} 

(A) L1 and L2 only
(B) L1 and L3 only
(C) L2 and L3 only
(D) L3 only

Answer: (B)
Explanation: We can build a push down automata for L1 and L3, but can not build push down automata for L@.

Note that a PDA can uses a stack. L1 and L3 can be identified using a single stack, but L2 can’t be.

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