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I have a question to solve but I am not even getting a direction to start or how to narrow down this problem. Please provide in your inputs.

Consider the following version of pumping lemma.

For any regular language $\mathcal L$, there is some $m≥1$ so that for every $y\in E^*$, if $|y|=m$, then there exist $u,x,v\in E^*$ so that:

  1. $y=uxv$
  2. $x \ne\epsilon$
  3. for all $z\in E^*$, $yz$ belongs to $\mathcal L$ if and only if $ux^ivz$ belongs to $\mathcal L$ for $i ≥0$

I need to prove that the pumping lemma holds. And language satisying i is regular

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    I tried it but something extra has to be done. I have a feeling it is related to Myhill Nerode and right invariant property. I am not sure. – 2012-06-11
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    This is just a roundabout way of expressing the pumping lemma for regular languages. Over at http://cs.stackexchange.com it is a [reference question](http://cs.stackexchange.com/questions/1031/how-to-prove-that-a-language-is-not-regular), and references [wikipedia](http://en.wikipedia.org/wiki/Pumping_lemma_for_regular_languages). – 2014-03-26

3 Answers 3