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Strongly locally testable semigroupswith commuting idempotentsand related languages

Published online by Cambridge University Press:  15 August 2002

Carla Selmi
Carla Selmi*
Affiliation:
LITP, Université de Paris VII, 2 place Jussieu, 75251 Paris Cedex 05, France, and Université de Rouen, Département d'Informatique, place Émile Blondel, 76128 Mont-Saint-Aignan Cedex, France; selmi@dir.univ-rouen.fr.
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Abstract

If we consider words over the alphabet which is the set of all elementsof a semigroup S, then such a word determines an element of S:the product of the letters of the word. S is strongly locally testable if whenever two words over thealphabet S have the same factors of a fixed length k, then the products of the letters of these words are equal. We had previously proved [19] thatthe syntactic semigroup of a rational language L is strongly locally testable if and only ifL is both locally and piecewise testable. We characterize in this paper the variety of strongly locally testable semigroups with commuting idempotents and, using the theory of implicit operations on avariety of semigroups, we derive an elementary combinatorial description of the related variety of languages.

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Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 33 , Issue 1 , January 1999 , pp. 47 - 57
Copyright
© EDP Sciences, 1999

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