Aperiodic finite state automaton
An aperiodic finite-state automaton (also called a counter-free automaton) is a finite-state automaton whose transition monoid is aperiodic. 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. In particular, the minimum automaton of a star-free language is always counter-free (however, a star-free language may also be recognized by other automata which are not aperiodic). 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""z" in "L" if and only if "xy""z" in "L". Another way to state Schützenberger's theorem is that star-free languages and counter-free languages are the same thing. An aperiodic automaton satisfies the Černý conjecture.