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Some results on C-varieties

Jean-Éric Pin, Howard Straubing (2010)

RAIRO - Theoretical Informatics and Applications

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 (a1a2...ak)+, where a1,...,ak are distinct letters. Next,...

Some results on 𝒞 -varieties

Jean-Éric Pin, Howard Straubing (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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 the notions...

Strongly automatic semigroups

Paul Mercat (2013)

Bulletin de la Société Mathématique de France

Dans cet article, nous introduisons la notion de semi-groupe fortement automatique, qui entraîne la notion d’automaticité des semi-groupes usuelle. On s’intéresse particulièrement aux semi-groupes de développements en base β , pour lesquels on obtient un critère de forte automaticité.

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