Problem Detail: Using pumping lemma, how can I prove that $L={a^n b^m c^k mid n = m vee mneq k}$ is not regular?. If I choose $w= a^m b^m c^m$ and pump up with $i=2$, if have $a^m=1 b^m c^m$ but the string is still in the language. Any hint?
Asked By : user3841581
Answered By : Yuval Filmus
The easiest way to show that $L$ isn’t regular is by noticing that $$ L cap b^+c^+ = { b^m c^k : m,k geq 1, m neq k }. $$ This should look familiar.
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