# Aperiodic finite state automaton

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Aperiodic finite state automaton

An aperiodic finite-state 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 celebrated result of algebraic automata theory is due to Marcel-Paul SchützenbergerSchützenberger, 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 conjectureTrahtman. "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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