I'm currently trying to figure out whether this language is context-free using the pumping lemma.
$\qquad L = \{ v_1 v_2 v_1 v_2 \mid v_1 \in \{a, b\}^*, v_2 \in \{a, c\}^* \}$
I'm having trouble because I don't know how to use the bound $m > 0$.
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"I'm currently trying to figure out whether this language is context-free using the pumping lemma." -- Reading this literally, it's impossible. The pumping lemma can only be used to show one of the two cases. I recommend you check out the relevant reference questions. – Raphael Aug 07 '17 at 14:15
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Welcome to Computer Science! Note that you can use LaTeX here to typeset mathematics in a more readable way. See here for a short introduction. – Raphael Aug 07 '17 at 14:15
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What specifically have you tried? It's hard to know what your problem with that bound is without you telling is what you did. (What does this bound refer to, anyway? What's $m$?) – Raphael Aug 07 '17 at 14:17
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Hint: Study how $L$ relates to ${ ww \mid w \in {0,1}^* } \not\in \mathrm{CFL}$. – Raphael Aug 07 '17 at 14:18
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What do you mean by "$m>0$"? That's the only $m$ in your question. – David Richerby Aug 07 '17 at 14:20