Aperiodic finite state automaton

Properties

A regular language is star-free if and only if it is accepted by an automaton with a finite and aperiodic transition monoid. This result of algebraic automata theory is due to Marcel-Paul Schützenberger.

A counter-free language is a regular language for which there is an integer n such that for all words x, y, z and integers m ≥ n we have xy^mz in L if and only if xyⁿz in L. A counter-free automaton is a finite-state automaton which accepts a counter-free language. A finite-state automaton is counter-free if and only if it is aperiodic.

An aperiodic automaton satisfies the Černý conjecture.