pumping lemma for $L=\{a^n b^m c^k \mid n = m \vee m\neq k\}$

Question

Using pumping lemma, how can I prove that $L=\{a^n b^m c^k \mid n = m \vee m\neq k\}$ 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?

I tried to improve your question, but there are still parts that do not make sense for me. — babou, May 07 '15 at 22:20

score 1 · Accepted Answer · answered May 07 '15 at 22:51

1

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.

answered May 07 '15 at 22:51

Yuval Filmus

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yes i do agree but what if i want to use the pumping lemma? – user3841581 May 09 '15 at 05:35
Then keep working on it. – Yuval Filmus May 09 '15 at 05:42
i think i got an idea; what if for a given m, we choose w=a^m b^m a^m; clearly this w is in L; and we can easily find the contradiction of the pumping lemma here – user3841581 May 09 '15 at 07:43

pumping lemma for $L=\{a^n b^m c^k \mid n = m \vee m\neq k\}$

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