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Equational description of pseudovarieties of homomorphisms

Published online by Cambridge University Press:  15 November 2003

Michal Kunc
Michal Kunc*
Affiliation:
Department of Mathematics, Masaryk University, Janáčkovo nám. 2a, 662 95 Brno, Czech Republic; URL: ; kunc@math.muni.cz.
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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.

Keywords

pseudovarietypseudoidentityimplicit operationvariety of regular languagessyntactic homomorphism.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 37 , Issue 3 , July 2003 , pp. 243 - 254
Copyright
© EDP Sciences, 2003

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References

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