Equational description of pseudovarieties of homomorphisms
Department of Mathematics, Masaryk University,
Janáčkovo nám. 2a, 662 95 Brno, Czech Republic;
Accepted: 3 September 2003
The notion of pseudovarieties of homomorphisms onto finite monoids was recently introduced by Straubing as an algebraic characterization for certain classes of regular languages. In this paper we provide a mechanism of equational description of these pseudovarieties based on an appropriate generalization of the notion of implicit operations. We show that the resulting metric monoids of implicit operations coincide with the standard ones, the only difference being the actual interpretation of pseudoidentities. As an example, an equational characterization of the pseudovariety corresponding to the class of regular languages in AC0 is given.
Mathematics Subject Classification: 20M35 / 68Q70
Key words: pseudovariety / pseudoidentity / implicit operation / variety of regular languages / syntactic homomorphism.
© EDP Sciences, 2003