Problem 4. [10 points] An alternative to Definition 7.2 in Linz for language acceptance is to require the stack to be empty when the end of the input string is reached. Formaly, an NPDA M is said to accept the language N(M) by empty stack if where p is any element in Q. Show that this notation is effectively equivalent to Definition 7.2 in the sense that for any NPDA M, there exists an NPDA M such that L(M)N(M), and vice versa