On varieties of meet automata

Authors:
Ondej Klíma;Libor Polák
Affiliations:
Department of Mathematics, Masaryk University, Janákovo nám 2a, 662 95 Brno, Czech Republic;Department of Mathematics, Masaryk University, Janákovo nám 2a, 662 95 Brno, Czech Republic
Venue:
Theoretical Computer Science
Year:
2008

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Abstract

Eilenberg's variety theorem gives a bijective correspondence between varieties of languages and varieties of finite monoids. The second author gave a similar relation between conjunctive varieties of languages and varieties of semiring homomorphisms. In this paper, we add a third component to this result by considering varieties of meet automata. We consider three significant classes of languages, two of them consisting of reversible languages. We present conditions on meet automata and identities for semiring homomorphisms for their characterization.