Problem Detail: I have a problem finding the right string to pump for the following language: $$L_1 = {a^{p+q}b^rc^sd^{q+r}e^s mid p, q, r, s ge 0}$$ Which string should I choose to pump? The problem is that I don’t know how to handle the fact that I have $p+q$ and $q+r$? Can I choose: $$Z = a^{2n}b^nc^nd^{2n}e^s$$ Thanks in advance.
Asked By : mrjasmin
Answered By : A.Schulz
If $k$ is the pump length from the regular pumping lemma choose $w=c^ke^k$. Clearly, $win L_1$, but if you pump you have to change the number of $c$’s while leaving the $e$’s unaltered. Hence after pumping the word is no longer a member of $L_1$.
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Question Source : http://cs.stackexchange.com/questions/7751
