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UGC-NET | UGC NET CS 2017 Jan – III | Question 23

  • Last Updated : 13 May, 2020

Given the following two languages :
L1 = {an bn | n ≥ 0, n ≠ 100}
L2 = {w ∈ {a, b, c}*| na(w) = nb(w) = nc(w)}
Which of the following options is correct ?
(A) Both L1 and L2 are not context free language
(B) Both L1 and L2 are context free language.
(C) L1 is context free language, L2 is not context free language.
(D) L1 is not context free language, L2 is context free language.


Answer: (C)

Explanation: Language L1 = {an bn | n ≥ 0, n ≠ 100} is context free because we push all the a^n into the stack and pop all b^n element for each a^n element since we can compare all a’s and b’s here using only one stack.

But language L2 = {w ∈ {a, b, c}*| na(w) = nb(w) = nc(w)} is not context free language because we can not compare all a’s, b’s and c’s simultaneously with the help of only one stack for this we need more then one stack here then this language L2 becomes context sensitive language.

Option (C) is correct.

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