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Consider the language: L = {a^(2+3k) or b^(10+12k)  } for k ≥ 0. Which of the following is correct
for the length of string L to satisfy Pumping Lemma?
(A) 5
(B) 24
(C) 9
(D) 3

Answer?

1 Answer

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6 votes
In the question, I have heard that they had asked for pumping length.

Answer will be 24.

But it is not the minimum pumping length. So I guess they just asked about pumping Length(which is any number for which pumping lemma condition is satisfied by the language) for this language.

Say P is the minimum Pumping length for a language..then every number greater than or equal to P is a Pumping Length for the language.

 

You could have simply eliminate the other three options by seeing that the minimal string in b is $b^{10}$ in the language. Now if  pumping Length were less than 10 then when we pump any part to power 0 of this string $b^{10}$.. then it doesn't belong to the language.

 

You didn't even need to solve this question if you knew the fact that " if P is a Pumping length for a language..then every number greater than or equal to P is a Pumping Length for the language."

 

I'll give full detailed explanation later when GATE 2019 Questions will be uploaded on GO.

 

Answer is 24.

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