Problem 8 Suppose V is a polynomial time verifier (see pages 293-294). That means there is a polynomial p(n), so that V decides whether to accept the pair (w,c) in time at most plu). We say V ": V accepts (w, c) for some c ?*). NP is exactly the class of languages with polynomial time verifiers. In our "guess-and-check" framework, you can think of w as the original input,c is the string that we "guess", and V does the "check" step. is a verifier for the language w E ? Suppose we change the definition, and we allow V to use p(Kw, c)) time (where p(n) is still some polynoi). With this modified definition, what class of languages do we get, instead of NP? (The issue is that c can now be much longer than w, and V will still have time to read it.) Problem 8 Suppose V is a polynomial time verifier (see pages 293-294). That means there is a polynomial p(n), so that V decides whether to accept the pair (w,c) in time at most plu). We say V ": V accepts (w, c) for some c ?*). NP is exactly the class of languages with polynomial time verifiers. In our "guess-and-check" framework, you can think of w as the original input,c is the string that we "guess", and V does the "check" step. is a verifier for the language w E ? Suppose we change the definition, and we allow V to use p(Kw, c)) time (where p(n) is still some polynoi). With this modified definition, what class of languages do we get, instead of NP? (The issue is that c can now be much longer than w, and V will still have time to read it.)