Editing State-transition table (section)

== Example ==
An example of a state-transition table together with the corresponding [[state diagram]] for a finite-state machine that accepts a string with an even number 0s is given below:

:{| class="wikitable" style="text-align: center; display: inline-table; vertical-align:top;"
|+ State-transition table
! {{diagonal split header|<small>Current state</small>|<small>Input</small>}}
! 0 !! 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>
|}
{| style="text-align: center; display: inline-table; vertical-align:top;"
|+ '''State diagram'''
|-
| [[File:FSM state diagram.png|200px|FSM state diagram]]
|}

In the state-transition table, all possible inputs to the finite-state machine are enumerated across the columns of the table, while all possible states are enumerated across the rows. If the machine is in the state S<sub>1</sub> (the first row) and receives an input of 1 (second column), the machine will stay in the state S<sub>1</sub>. Now if the machine is in the state S<sub>1</sub> and receives an input of 0 (first column), the machine will transition to the state S<sub>2</sub>.<br>
In the state diagram, the former is denoted by the arrow looping from S<sub>1</sub> to S<sub>1</sub> labeled with a 1, and the latter is denoted by the arrow from S<sub>1</sub> to S<sub>2</sub> labeled with a 0. This process can be described statistically using [[Markov Chains]].

For a [[Nondeterministic finite automaton|nondeterministic finite-state machine]], an input may cause the machine to be in more than one state, hence its [[Nondeterministic programming|non-determinism]]. This is denoted in a state-transition table by the set of all target states enclosed in a pair of braces {}. An example of a state-transition table together with the corresponding state diagram for a nondeterministic finite-state machine is given below:

:{| class="wikitable" style="text-align: center; display: inline-table; vertical-align:top;"
|+ State-transition table
! {{diagonal split header|<small>Current state</small>|<small>Input</small>}}
! 0 !! 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>} || S<sub>2</sub>
|}
{| style="text-align: center; display: inline-table; vertical-align:top;"
|+ '''State diagram'''
|-
| [[File:NFSM state diagram.png|200px|NFSM state diagram]]
|}

If the machine is in the state S<sub>2</sub> and receives an input of 0, the machine will be in two states at the same time, the states S<sub>1</sub> and S<sub>2</sub>.