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Construct a push-down automata to recognize the language $ A = \{u\#v \in \{0,1,\#\}^{*} | u = v^{\complement} \} $. Here, $v^{\complement}$ is the bit-complement of v.

I don't see how to perform this with a LIFO stack. I would like some hints (not a solution) if possible.

Thanks,

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There is no such PDA because $A$ is not context-free. This can be proved by pumping.

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