(Solved): (10 points) A useless state in a pushdown automata is never entered on any input string. Consider t ...

(10 points) A useless state in a pushdown automata is never entered on any input string. Consider the problem of determine whether a pushdown automata has any useless states. Formulate this problem as a language and show that it is decidable. Hint: Think about some of properties we learned about context-free grammars.