Finite State Machine / Finite State Automation

A finite state machine or automation provides a simple model of computation, a way to reduce the complexities of a computer to its essence, in addition to its theoretical significance this can be a good way to tackle certain types of practical problem.

finite state machine automation

The current state is determined by past states of the system and the inputs to the system (it has a memory). A transition indicates a state change and is described by a condition that would need to be fulfilled to enable the transition. An action is a description of an activity that is to be performed at a given moment.

State diagram

We could describe the machine in terms of transitions, for each combination of state and input this will determine the transition function which gives the next state:

state diagram

State transition table

Condition↓Current state → State 1 State 2 State 3 State 4 State 5 State 6
Input red State 2 State 3 State 1 State 5 State 6 State 4
Input blue State 4 State 5 State 6 State 1 State 2 State 3

Outputs

There are different variants, for instance,

Mathematical Model

In its essence the model consists of (Σ,S,s0,δ), where:

In some circumstances (for instance Mealy machine) we may need to add:


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