The study of the mathematical properties of such automata is automata theory. The picture is a visualization of an automaton that recognizes strings containing an even number of 0s. The automaton starts in state S1, and transitions to the non-accepting state S2 upon reading automata theory and computability pdf symbol 0.

Reading another 0 causes the automaton to transition back to the accepting state S1. In both states the symbol 1 is ignored by making a transition to the current state. Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them. Greek word αὐτόματα, which means “self-acting”.

The figure at right illustrates a finite-state machine, which belongs to a well-known type of automaton. Automata theory is closely related to formal language theory.

An automaton is a finite representation of a formal language that may be an infinite set. Automata are often classified by the class of formal languages they can recognize, typically illustrated by the Chomsky hierarchy which describes the relations between various languages and kinds of formalized logic.

Automata play a major role in theory of computation, compiler construction, artificial intelligence, parsing and formal verification. An automaton is a construct made of states designed to determine if the input should be accepted or rejected. It looks a lot like a basic board game where each space on the board represents a state.