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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 lemma) for L?
  • a)
    3
  • b)
    5
  • c)
    9
  • d)
    24
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
For Σ = {a, b}, let us consider the regular language L = {x|x = ...
Regular language L = {x|x = a2+3k or x = b10+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 wi = 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.
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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 lemma) for L?a)3b)5c)9d)24Correct answer is option 'D'. Can you explain this answer?
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