If computation on a PDA reaches a final state with an empty stack, will it immediately accept, regardless of whether or not the input tape has ended. For example if I have a PDA to recognize the language of strings where $a^nb^n$, if it was fed the string aaabbba, will it stop after seeing the last b if the stack were empty and it was in an accept state? Or would the PDA, need to specify a dead state from the final state for incorrect strings?For example, this PDA would seem to accept aaabbba:
Does a PDA immediately accept if at final state with empty stack?
pushdown automata
There are two ways in which a PDA may accept:Final state: The PDA has finished reading the input and it is in the final stateEmpty stack: The PDA has finished reading the input and its stack is empty.The PDA in the example you have provided is non-deterministic, and when non-deterministic systems read an input for which a transition is not defined, they get stuck. In this case, when the PDA reads the string aaabbba, it would get stuck after reading the last b.