- Aperiodic finite state automaton
An

**aperiodic finite-state automaton**is afinite-state automaton whosetransition monoid is aperiodic.**Properties**A

regular language is star-free if and only if it is accepted by an automaton with a finite and aperiodictransition monoid . This celebrated result of algebraicautomata theory is due toMarcel-Paul Schützenberger Schützenberger, Marcel-Paul, "On finite monoids having only trivial subgroups," "Information and Control", Vol 8 No. 2, pp. 190-194, 1965.] .An aperiodic automaton satisfies the

Cerny conjecture Trahtman. "The Cerny conjecture for aperiodic automata," "Discrete Mathematics and Theoretical Computer Science," Vol 9 No. 2, pp. 133-138, 2007.] .**References**

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