$L_1 = (a^k * b^r \mid k \neq r^2)$
$L_2 = (a ^{\sum_i ^n t} \mid n > 0 )$
How to prove by pumping lemma these languages are not regular?
1
$\begingroup$
automata
regular-language
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1I'm not 100% sure I interpreted "(a ^(sigma from i to n) t | n > 0 )" correctly. Please switch it if I'm wrong. For one thing, the $t$ seems strange. – 2012-12-21
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0Are you sure that $i$ in the definition of $L_2$ isn't supposed to be $1$? It would make more sense, since if $i > 1$, we'd need to pick some meaningful definition for $\sum_{t=i}^n$ when $n < i$. – 2012-12-23