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I'm asking myself if the problem of decide whether a push down automaton will accept a word is decidable.
I would say that you can simulate a push down automaton with a Turing Machine and, if it doesn't loop forever, accept the word when the automaton accepts, or reject when it does. In this case, the problem of decide if a push down automaton accept a word would be semi-decidable. But I'm not sure if that is correct and also, I can't find a way to prove if it is decidable or not.
Any ideas here?