Non-deterministic finite automaton (NFA) definition

Non-deterministic automaton is different from a deterministic one in that it can contain multiple transitions of the same letter from one state to other(s)

The second difference is that states can have no transitions with some letters. The absence of such a transfer means that the automaton can be “stopped” by sending input that arrives to such a state and tries to continue to a non-existing transfer

The language of such an automaton is defined as follows: Word is part of automaton language if and only if there exists a sequence of transitions such that automaton finishes in the accepting state







Stronger non-determinism

Equivalence of DFA and NFA theorem



NFA with transitions definition

This is a variation of a non-deterministic automaton that allows changing the state without reading any input, it is denoted as a transition. This allows us to build complex automata much more easily! For example a union of automata can be built as a “sum” of automata and a new start state, that has transitions to all start states of each automaton

Closure definition

Equivalence of NFA and NFA with transitions theorem