Editing Nondeterministic finite automaton (section)

===Example===
[[Image:NFAexample.svg|thumb|250px|The [[state diagram]] for ''M'']]
Let <math>M</math> be a NFA-ε, with a binary alphabet, that determines if the input contains an even number of 0s or an even number of 1s. Note that 0 occurrences is an even number of occurrences as well.

In formal notation, let <math display=block>M = (\{S_0, S_1, S_2, S_3, S_4\}, \{0, 1\}, \delta, S_0, \{S_1, S_3\})</math> where
the transition relation <math>\delta</math> can be defined by this [[state transition table]]:
{| class="wikitable" style="margin-left:auto;margin-right:auto; text-align:center;"
! {{diagonal split header|State|Input}}
! 0
! 1
! ε
|-
! ''S''<sub>0</sub>
| {}
| {}
| {''S''<sub>1</sub>, ''S''<sub>3</sub>}
|-
! ''S''<sub>1</sub>
| {''S''<sub>2</sub>}
| {''S''<sub>1</sub>}
| {}
|-
! ''S''<sub>2</sub>
| {''S''<sub>1</sub>}
| {''S''<sub>2</sub>}
| {}
|-
! ''S''<sub>3</sub>
| {''S''<sub>3</sub>}
| {''S''<sub>4</sub>}
| {}
|-
! ''S''<sub>4</sub>
| {''S''<sub>4</sub>}
| {''S''<sub>3</sub>}
| {}
|}
<math>M</math> can be viewed as the union of two [[deterministic finite automaton|DFA]]s: one with states <math>\{S_1, S_2\}</math> and the other with states <math>\{S_3, S_4\}</math>. 
The language of <math>M</math> can be described by the [[regular language]] given by this [[regular expression]] <math>(1^{*}01^{*}01^{*})^{*} \cup (0^{*}10^{*}10^{*})^{*}</math>.
We define <math>M</math> using ε-moves but <math>M</math> can be defined without using ε-moves.