What is wrong with the following (faulty) "proof" that LHALT E NP? ro0 Or as follows: V"On input ((M), x), k): 1. Run M on input r for up to k steps. 2. If M halts within these k steps, accept; otherwise, reject." "Analysis": If (M),x) E LHALT, then M must halt on x after some finite number of steps k, which means that V((M), x), k) will accept. And if (M), x) LHALT, then V will reject no matter what certificate k is provided. Therefore, V is an efficient verifier for LHALT, So HALT E NP