# Automata - Finite Automata

A finite automaton is an automaton that has a set of states and its control moves from state to state in response to external inputs.

It has a start and an end state and there are only a finite number of states

## Definition

A formal de definition of a finite automaton is whenever:

• an input X is received by an automaton,
• the automaton must follow an arc labeled X from the state it is in to some new state (for all states)

## Example

### Lexer

An automaton implementing a lexer modeling the recognition of the keyword then

where:

• the state (circle) represents a different position in the word then that has been reached so far that ranges from:
• the empty string (ie nothing)
• to the complete word

## Implementation

The advantage of having only a finite number of states is that we can implement the system with a fixed set of resources

Example:

• Hardware: we could implement it in hardware as a circuit
• Software: to make the decision
• looking at the state
• or using the position in the code itself

### Model

example: A on/off button

## Documentation / Reference

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