Editing Nondeterministic finite automaton (section)

==Properties==
The machine starts in the specified initial state and reads in a string of symbols from its [[Alphabet (computer science)|alphabet]]. The automaton uses the [[state transition function]] Δ to determine the next state using the current state, and the symbol just read or the empty string. However, "the next state of an NFA depends not only on the current input event, but also on an arbitrary number of subsequent input events. Until these subsequent events occur it is not possible to determine which state the machine is in".<ref>FOLDOC Free Online Dictionary of Computing, ''[http://foldoc.org/nfa Finite-State Machine]''</ref> If, when the automaton has finished reading, it is in an accepting state, the NFA is said to accept the string, otherwise it is said to reject the string.

The set of all strings accepted by an NFA is the language the NFA accepts. This language is a [[regular language]].

For every NFA a [[deterministic finite automaton]] (DFA) can be found that accepts the same language. Therefore, it is possible to convert an existing NFA into a DFA for the purpose of implementing a (perhaps) simpler machine. This can be performed using the [[powerset construction]], which may lead to an exponential rise in the number of necessary states. For a formal proof of the powerset construction, please see the [[Powerset construction]] article.