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I have a vital misunderstanding of the pumping lemma. In the following example I show an example of using it on a regular language to come to incorrect conclusions. What am I doing wrong?

L={a*b*}, assume the language is regular so by the pumping lemma there exists some n, and σ = αβγ and σ' = αβ^kγ ∈ L for all non negative k.

σ = aaabbb

α = aa

β = ab

γ = bb

then σ'= αβ^2γ for k=2, σ' =aaababbb

σ'∉ L, a contradiction, thus L is not regular.

L as described I know to be a regular language so I would expect to find ∈ L. This is due to my choice of β spanning across two characters but there is nothing I can find in the pumping lemma which forbids this.

Bharti Rawat
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Karl
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  • I'm voting to close this question as off-topic because is it not (yet) a computer programming question. It's a question about the theory of regular languages. – Raymond Chen Jun 11 '19 at 13:35
  • my mistake. I asked the question again here: https://cs.stackexchange.com/questions/110527/using-pumping-lemma-to-prove-irregulairt-of-regular-language-what-is-my-error – Karl Jun 11 '19 at 13:57

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