Editing Deterministic finite automaton (section)

==Example==
The following example is of a DFA {{mvar|M}}, with a binary alphabet, which requires that the input contains an even number of 0s.

[[File:DFAexample.svg|right|thumb|upright=1.1|The [[state diagram]] for ''M'']]
{{math|1=''M'' = (''Q'', Σ, ''δ'', ''q''<sub>0</sub>, ''F'')}} where
*{{math|1=''Q'' = {''S''<sub>1</sub>, ''S''<sub>2</sub>}<nowiki/>}}
*{{math|1=Σ = {0, 1}<nowiki/>}}
*{{math|1=''q''<sub>0</sub> = ''S''<sub>1</sub>}}
*{{math|1=''F'' = {''S''<sub>1</sub>}<nowiki/>}} and
*{{mvar|δ}} is defined by the following [[state transition table]]:
:{| border="1" cellpadding="1" cellspacing="0"
| || {{center|'''0'''}} || {{center|'''1'''}}
|-
|'''''S''<sub>1</sub>''' || ''S''<sub>2</sub> || ''S''<sub>1</sub>
|-
|'''''S''<sub>2</sub>''' || ''S''<sub>1</sub> || ''S''<sub>2</sub>
|}

The state {{math|''S''<sub>1</sub>}} represents that there has been an even number of 0s in the input so far, while {{math|''S''<sub>2</sub>}} signifies an odd number. A 1 in the input does not change the state of the automaton. When the input ends, the state will show whether the input contained an even number of 0s or not. If the input did contain an even number of 0s, {{mvar|M}} will finish in state {{math|''S''<sub>1</sub>}}, an accepting state, so the input string will be accepted.

The language recognized by {{mvar|M}} is the [[regular language]] given by the [[regular expression]] <code>(1*) (0 (1*) 0 (1*))*</code>, where <code>*</code> is the [[Kleene star]], e.g., <code>1*</code> denotes any number (possibly zero) of consecutive ones.