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Concept
State-transition table
Summary
In automata theory and sequential logic, a state-transition table is a table showing what state (or states in the case of a nondeterministic finite automaton) a finite-state machine will move to, based on the current state and other inputs. It is essentially a truth table in which the inputs include the current state along with other inputs, and the outputs include the next state along with other outputs.
A state-transition table is one of many ways to specify a finite-state machine. Other ways include a state diagram.
State-transition tables are sometimes one-dimensional tables, also called characteristic tables. They are much more like truth tables than their two-dimensional form. The single dimension indicates inputs, current states, next states and (optionally) outputs associated with the state transitions.
{| class="wikitable" style="text-align: center;"
|+ State-transition table(S: state, I: input, O: output)
|-
! Input !! Current state !! Next state !! Output
|-
| I1 || S1 || Si || Ox
|-
| I2 || S1 || Sj || Oy
|-
| ... || ... || ... || ...
|-
| In || S1 || Sk || Oz
|-
| I1 || S2 || Si′ || Ox′
|-
| I2 || S2 || Sj′ || Oy′
|-
| ... || ... || ... || ...
|-
| In || S2 || Sk′ || Oz′
|-
| ... || ... || ... || ...
|-
| I1 || Sm || Si′′ || Ox′′
|-
| I2 || Sm || Sj′′ || Oy′′
|-
| ... || ... || ... || ...
|-
| In || Sm || Sk′′ || Oz′′
|}
State-transition tables are typically two-dimensional tables. There are two common ways for arranging them.
In the first way, one of the dimensions indicates current states, while the other indicates inputs. The row/column intersections indicate next states and (optionally) outputs associated with the state transitions.
{| class="wikitable" style="text-align: center;"
|+ State-transition table(S: state, I: input, O: output)
! !! I1 !! I2 !! ... !! In
|-
! S1
| Si/Ox || Sj/Oy || ... || Sk/Oz
|-
! S2
| Si′/Ox′ || Sj′/Oy′ || ... || Sk′/Oz′
|-
! ...
| ... || ... || ... || ...
|-
! Sm
| Si′′/Ox′′ || Sj′′/Oz′′ || ... || Sk′′/Oz′′
|}
In the second way, one of the dimensions indicates current states, while the other indicates next states.
Official source
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