Editing Nondeterministic finite automaton (section)

===Extended transition function===
Similar to NFA without ε-moves, the transition function <math>\delta</math> of an NFA-ε can be extended to strings.
Informally, <math>\delta^*(q,w)</math> denotes the set of all states the automaton may have reached when starting in state <math>q \in Q</math> and reading the string <math>w \in \Sigma^* .</math>
The function <math>\delta^*: Q \times \Sigma^* \rightarrow \mathcal{P}(Q)</math> can be defined recursively as follows.
* <math>\delta^*(q,\varepsilon) = E(q)</math>, for each state <math>q \in Q ,</math> and where <math>E</math> denotes the epsilon closure;
:''Informally:'' Reading the empty string may drive the automaton from state <math>q</math> to any state of the epsilon closure of <math>q .</math>
* <math display=inline>\delta^*(q,wa) = \bigcup_{r \in \delta^*(q,w)} E(\delta(r,a)) ,</math> for each state <math>q \in Q ,</math> each string <math>w \in \Sigma^*</math> and each symbol <math>a \in \Sigma .</math>
:''Informally:'' Reading the string <math>w</math> may drive the automaton from state <math>q</math> to any state <math>r</math> in the recursively computed set <math>\delta^*(q,w)</math>; after that, reading the symbol <math>a</math> may drive it from <math>r</math> to any state in the epsilon closure of <math>\delta(r,a) .</math> 

The automaton is said to accept a string <math>w</math> if 
:<math>\delta^*(q_0,w) \cap F \neq \emptyset ,</math> 
that is, if reading <math>w</math> may drive the automaton from its start state <math>q_0</math> to some accepting state in <math>F .</math>{{sfn|Hopcroft|Ullman|1979|p=25}}