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| HAL : hal-00019824, version 1 |
| Fiche détaillée |  Récupérer au format |
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| International Journal of Algebra and Computation 1 (1991) 291-314 |
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| Semigroups whith idempotent stabilizers and applications to automata theory |
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| Bertrand Le Saec 1Jean-Eric Pin 2 |
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| (1991) |
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| We show that every finite semigroup is a quotient of a finite semigroup in which every right stabilizer satisfies the identities x = x^2 and xy = xyx. This result has several consequences. We first give a geometrical application : every finite transformation semigroup has a fixpoint-free covering (a transformation semigroup is fixpoint-free if every element which stabilizes a point is idempotent). Next we use our result and a result of I. Simon on congruences on paths to obtain a purely algebraic proof of a deep theorem of McNaughton on infinite words. Finally, we give an algebraic proof of a theorem of Brown on a finiteness condition for semigroups. |
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| 1 : | Laboratoire Bordelais de Recherche en Informatique (LaBRI) |
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CNRS : UMR5800 – Université Sciences et Technologies - Bordeaux I – École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB) – Université Victor Segalen - Bordeaux II |
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| 2 : | Laboratoire d'informatique Algorithmique : Fondements et Applications (LIAFA) |
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CNRS : UMR7089 – Université Paris VII - Paris Diderot |
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| Automates et Applications |
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| Domaine | : | Informatique/Autre |
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| finite semigroup – infinite words – stabilizer |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00019824, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00019824 | |
| oai:hal.archives-ouvertes.fr:hal-00019824 | |
| Contributeur : Jean-Eric Pin | |
| Soumis le : Mardi 28 Février 2006, 11:26:53 | |
| Dernière modification le : Mardi 28 Février 2006, 21:21:19 | |
