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A classification of rational languages by semilattice-ordered
monoids

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*Libor Polak*

**Address.**

Department of Mathematics, Masaryk University, Janackovo nam. 2a, 662 95 Brno, Czech Republic

**E-mail. **polak@math.muni.cz

**Abstract.**

We prove here an Eilenberg type theorem: the so-called
conjunctive varieties of rational languages correspond to the
pseudovarieties of finite semilattice-ordered monoids.
Taking complements of members of a conjunctive variety of languages
we get a so-called disjunctive variety. We present here a non-trivial
example of such a variety together with an equational characterization of the
corresponding pseudovariety.

**AMSclassification. **Primary: 68Q70;
Secondary: 20M07, 06F05.

**Keywords. ** Syntactic semilattice-ordered monoid, conjunctive varieties of rational languages.