Displaying similar documents to “Some results on C-varieties”

Equational description of pseudovarieties of homomorphisms

Michal Kunc (2010)

RAIRO - Theoretical Informatics and Applications

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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...

Some results on 𝒞 -varieties

Jean-Éric Pin, Howard Straubing (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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In an earlier paper, the second author generalized Eilenberg’s variety theory by establishing a basic correspondence between certain classes of monoid morphisms and families of regular languages. We extend this theory in several directions. First, we prove a version of Reiterman’s theorem concerning the definition of varieties by identities, and illustrate this result by describing the identities associated with languages of the form ( a 1 a 2 ⋯ a k ) + , where a 1 , ... , a k are distinct letters. Next, we generalize...

Krohn-Rhodes complexity pseudovarieties are not finitely based

John Rhodes, Benjamin Steinberg (2010)

RAIRO - Theoretical Informatics and Applications

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We prove that the pseudovariety of monoids of Krohn-Rhodes complexity at most is not finitely based for all . More specifically, for each pair of positive integers , we construct a monoid of complexity , all of whose -generated submonoids have complexity at most .

Binary relations on the monoid of V-proper hypersubstitutions

Klaus Denecke, Rattana Srithus (2006)

Discussiones Mathematicae - General Algebra and Applications

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In this paper we consider different relations on the set P(V) of all proper hypersubstitutions with respect to a given variety V and their properties. Using these relations we introduce the cardinalities of the corresponding quotient sets as degrees and determine the properties of solid varieties having given degrees. Finally, for all varieties of bands we determine their degrees.