非确定性有限自动机接受和拒绝

Question

Can an NFA ever accept a string which is not in the language? I know that for an NFA to accept a string there has to be atleast one way by which it gets accepted and we can safely say that the NFA accepts it. But in case of Rejection ...can at times it may happen that if a string which doesn't belong to the language getting accepted by NFA?

Answer 1

The definition of the language accepted by an NFA says that it is the set of all strings that are accepted by the NFA. So clearly, every string that is accepted belongs to the language, and thus the answer to your question is: No.

Rejection means: all possible computations for the given string either end in a non-accepting state or do not even read the entire string (if the automaton is not complete). Both of these possibilities exclude acceptance.

For non-deterministic Turing Machines there exist notions of acceptance like: "more than half of the computations accept," or "an odd number of computations accept" ( Parity ) etc. There you can have accepting computations despite global rejection. But these notions are not widely used and I have never seen them applied to finite automata.