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:
- $y=uxv$
- $x \ne\epsilon$
- 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