For Σ = {a, b}, let us consider the regular language L = {x|x = a2+3kor x = b10+12kk ≥ 0}.Which one of the following can be a pumping length (the constant guaranteed by the pumping lemma) for L?a)3b)5c)9d)24Correct answer is option 'D'. Can you explain this answer?

Question

For &Sigma; = {a, b}, let us consider the regular language L = {x|x = a2+3kor x = b10+12kk &ge; 0}.Which one of the following can be a pumping length (the constant guaranteed by the pumping lemma) for L?a)3b)5c)9d)24Correct answer is option 'D'. Can you explain this answer?

Answer

Regular language L = {x|x = a^2+3k or x = b^10+12k k ≥ 0}.

L = {a², a⁵, a⁸, a¹¹ … ∪ b¹⁰, b²², b³⁴…}

Pumping Lemma:

Let L be an infinite regular language. Then there exists some positive integer m such that any w ϵ L with |w|≥ m can be decomposed as

w = xyz

with |xy|≤ m such that w_i = xyⁱz

is also L for all i = 0, 1, 2, …

Therefore, minimum Pumping Length should be 11, because string with length 10 (i.e., w = b¹⁰) does not repeat anything, but string with length 11 (i.e., w = b¹¹) will repeat states.

Hence option 1, 2, and 3 are eliminated.

Therefore 24 can be the pumping lemma length.

Answer

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Similar Computer Science Engineering (CSE) Doubts

For Σ = {a, b}, let us consider the regular language L = {x|x = a2+3k or x = b10+12k k ≥ 0}.Which one of the following can be a pumping length (the constant guaranteed by the pumping lemm

For ∑ = {a,b} , let us consider the regular language L = {x | x a2+3kor x = b10+12k, k≥ 0}.Which one of the following can be a pumping length (the constant guaranteed by the pumping lemm

A language L satisfies the Pumping Lemma for regular languages, and also the Pumping Lemma for context-free languages. Which of the following statements about L is TRUE?

Which of the following is/are FALSE regarding pumping lemma for regular languages?

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