syntactic semilattice-ordered monoid; conjunctive varieties of rational languages
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.
 Myhill J.: Finite automata and the representation of events. WADD Techn. Report 57–624, Wright Patterson Air Force Base, 1957.
 Pin J.-E.: A variety theorem without complementation
. Izvestiya VUZ Matematika 39 (1995), 80–90. English version: Russian Mathem. (Iz. VUZ) 39 (1995), 74–83. MR 1391325
 Polák L.: Syntactic semiring of a language
. in Proc. Mathematical Foundation of Computer Science 2001, Lecture Notes in Comput. Sci., Vol. 2136 (2001), 611–620. Zbl 1005.68526
 Polák L.: Operators on Classes of Regular Languages
. in Algorithms, Automata and Languages, J.P.G. Gomes and P. Silva (ed.), World Scientific (2002), 407–422. MR 2023799
 Polák L.: Syntactic Semiring and Language Equations
. in Proc. of the Seventh International Conference on Implementation and Application of Automata, Tours 2002, Lecture Notes in Comput. Sci., Vol. 2608 (2003), 182–193. MR 2047726
 Straubing H.: On logical descriptions of regular languages
. in Proc. LATIN 2002, Lecture Notes in Comput. Sci., Vol. 2286 (2002), 528–538. MR 1966148
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