An automaton or sequential machine is a discrete and usually finite system that proceeds sequentially from an initial state to a final discrete state upon changing its inputs, and that also produces an output at each step determined by the input and the internal state of the automaton. An automaton thus defined has a state space which is a finite semigroup or monoid, and that can be decomposed into certain types of modules or parts in a canonical manner. Two functions or maps usually determine mathematically the functioning of the automaton : the transition function from one state to the next, and the ouput function that maps an input and a specific state to a specific output of the automaton. Examples of automata are abundant as machines, computers and robots. Their underlying operational logic is Boolean. Exceptions are fuzzy systems based on 'fuzzy logic'.
Automata are very useful automation tools.