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### Prove not context free

How can we prove that: $$L = \{ w_1\#w_2 \mid w_1 \in w_2;\; |w_2| > |w_1|;\; w_1 , w_2 \in \{0, 1\}^*\}$$ is not context-free? The language defines $w_1$ as a sub-string of $w_2$, and they ...
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### Complement and Context Free Surprising

Anyone can describe why $L_{1}$ is not the complement of $L_{2}$, and why $L_{2}$ is not context free? $$L_{1}= \{w_{1}cw_{2} : w_{1},w_{2} \in \{a,b\}^{\ast}, w_{1} \neq w_{2}\}$$ L_{2}= \{w_{1}...
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### Can the String, $0^p 0^p 0^p$, be Used with the Pumping Lemma to Show that $w^r w w^r$ is Not Context Free?

I'm trying to show that $L=\left\{w^rww^r:w \in \{0,1\}^*\right\}$ is not context free using the pumping lemma. I thought picking the string, $0^p0^p0^p$, would be a good candidate for this, but ...
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### Can the pumping lemma for context free languages be extended to any subword?

It is known that in the case of a Regular Language $L$ , the pumping lemma can be extended to apply to any sufficiently long subword of the language, ie, if $uwv \in L$ and $|w| \ge p$ then we can ...
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### Does a pushdown automata exists for the following language?

I have came across a question stating that language $L = a^n b^n c^{2n}$ is not a context free language and hence, no PDA can be constructed for it. But what I am wondering is that, if I add another ...
How are these Context-Free Pumping Lemma Approaches differ? Maybe this might help understand pumping lemma better $(a^{i}b^{i}c^{j}d^{j} \mid i, j \geq 0$} $(a^{i}b^{j}c^{i}d^{j} \mid i, j \geq 0$} ...
I am trying to use the pumping lemma to show this language is not context free: $L = a^nb^{n+1}c^{2n} : n \ge 0$ So I took $z = a^mb^{m+1}c^{2m}$ where $|z| = 4m+1 > m$. We can decompose \$z = a^mb^...