Equational description of pseudovarieties of homomorphisms

KUNC, Michal. Equational description of pseudovarieties of homomorphisms. RAIRO - Theoretical Informatics and Applications. Les Ulis (Francie): EDP Sciences, 2003, vol. 37, No 3, p. 243-254. ISSN 0988-3754.

Basic information

• Original name: Equational description of pseudovarieties of homomorphisms
• Authors: KUNC, Michal (203 Czech Republic, guarantor).
• Edition: RAIRO - Theoretical Informatics and Applications, Les Ulis (Francie), EDP Sciences, 2003, 0988-3754.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10101 Pure mathematics
• Country of publisher: France
• Confidentiality degree: is not subject to a state or trade secret
• WWW: URL
• Impact factor: Impact factor: 0.154 in 2001
• RIV identification code: RIV/00216224:14310/03:00008400
• Organization unit: Faculty of Science
• UT WoS: 000187672500002
• Keywords in English: Pseudovariety; Pseudoidentity; Implicit operation; Variety of regular languages; Syntactic homomorphism
• Tags: Implicit operation, Pseudoidentity, Pseudovariety, Syntactic homomorphism, Variety of regular languages

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.

Links

• GA201/01/0323, research and development project: Name: Ekvacionální logika pologrup a aplikace

Investor: Czech Science Foundation, Equational logic of semigroups and applications