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Topologie p -adique sur les mots

Jean-Éric Pin — 1993

Journal de théorie des nombres de Bordeaux

Cet article est une introduction aux aspects combinatoires de la distance p -adique et de la topologie p -adique sur les mots. On donne plusieurs définitions équivalentes de ces notions, illustrées par divers exemples et propriétés. Après avoir décrit de façon détaillée les ouverts, on démontre que la distance p -adique est uniformément équivalente à une distance obtenue à partir des coefficients binomiaux définis sur les mots. On donne également deux exemples de suites convergentes dans la topologie...

Some results on 𝒞 -varieties

Jean-Éric PinHoward 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...

A conjecture on the concatenation product

Jean-Eric PinPascal Weil — 2001

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

In a previous paper, the authors studied the polynomial closure of a variety of languages and gave an algebraic counterpart, in terms of Mal’cev products, of this operation. They also formulated a conjecture about the algebraic counterpart of the boolean closure of the polynomial closure – this operation corresponds to passing to the upper level in any concatenation hierarchy. Although this conjecture is probably true in some particular cases, we give a counterexample in the general case. Another...

Some results on -varieties

Jean-Éric PinHoward 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 , where are distinct letters. Next,...

A conjecture on the concatenation product

Jean-Eric PinPascal Weil — 2010

RAIRO - Theoretical Informatics and Applications

In a previous paper, the authors studied the polynomial closure of a variety of languages and gave an algebraic counterpart, in terms of Mal'cev products, of this operation. They also formulated a conjecture about the algebraic counterpart of the boolean closure of the polynomial closure – this operation corresponds to passing to the upper level in any concatenation hierarchy. Although this conjecture is probably true in some particular cases, we give a counterexample in the general case....

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