On varieties of meet automata

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. Key words: varieties of languages, varieties of meet automata, varieties of semiring homomorphisms

• Type: Journal
• Year: 2008
• Where: TCS
• Authors: Ondrej Klíma, Libor Polák
• Keywords: Bijective Correspondence, Conjunctive Varieties, TCS 2008, Theoretical Computer Science, Variety Theorem