Automata - Finite Automata

1 - About

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

3 - 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)

3.1 - Class

4 - Example

4.1 - 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

4.2 - Others

5 - 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

5.1 - Model

example: A on/off button

6 - Documentation / Reference


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