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Semigroups defined by automaton extension mapping

Mirosław Osys (2005)

Discussiones Mathematicae - General Algebra and Applications

We study semigroups generated by the restrictions of automaton extension (see, e.g., [3]) and give a characterization of automaton extensions that generate finite semigroups.

Some Algebraic Properties of Machine Poset of Infinite Words

Aleksandrs Belovs (2008)

RAIRO - Theoretical Informatics and Applications

The complexity of infinite words is considered from the point of view of a transformation with a Mealy machine that is the simplest model of a finite automaton transducer. We are mostly interested in algebraic properties of the underlying partially ordered set. Results considered with the existence of supremum, infimum, antichains, chains and density aspects are investigated.

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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