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I was just putting some thought into different languages (as I’m reviewing for final exams coming up) and I can not think of a valid pushdown automata to handle the language A = {0^n 1^n 0^n | n >= 0}. This is not a context-free language, am I correct?
I believe you are. It looks quite similar to the language L = { a^i b^i c^i | i > 0 } which the Wikipedia article on the pumping lemma uses as an example of how to prove that a language is not context-free.