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Equational description of pseudovarieties of homomorphisms

Published online by Cambridge University Press:  15 November 2003

Michal Kunc*
Affiliation:
Department of Mathematics, Masaryk University, Janáčkovo nám. 2a, 662 95 Brno, Czech Republic; URL: ; [email protected].
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Abstract

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.

Type
Research Article
Copyright
© EDP Sciences, 2003

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