Let A = {(B,w) | B is an NFA that accepts w}. To prove that N is a decidable language,
M = "on input (B,w) where B is NFA and w is a string, simulate B on w. If B accepts w, accept. Otherwise, reject"
Is this a false proof? The proof from the textbook says that I have to convert NFA into equivalent DFA but I'm not sure why this would be necessary. Is it not possible to simulate NFA directly without conversion?