This is a question that has emerged from a recent quiz I have taken. In short
Consider the following transitions on a push down automaton. Assume the starting state is q. Which one of the following inputs will lead the automaton to state p with the stack containing the string XXZ?
I am gonna write only the transitions from state q regardless of the input symbol:
(q, 0, Z) -> (q, XZ) (q, 0, X) -> (q, XX) (q, 1, X) -> (q, X) (q, ε, Χ) -> (p, ε)
Now the thing we note here is that there is no transition from state q when there is an empty stack regardless of the input symbol. How does one answer that question assuming we start from an empty stack? I have omitted the inputs cause I don't really care about the answer to the quiz, all I want to know is how would someone start working on that?