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| HAL : hal-00017406, version 1 |
| DOI : 10.1007/11523468_33 |
| Fiche détaillée |  Récupérer au format |
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| (2005) |
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| On the equivalence of Z-automata |
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| Marie-Pierre Béal 1Sylvain Lombardy 2 |
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| (2005) |
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| We prove that two automata with multiplicity in Z are equivalent, i.e. define the same rational series, if and only if there is a sequence of Z-coverings, co-Z-coverings, and circulations of –1, which transforms one automaton into the other. Moreover, the construction of these transformations is effective. This is obtained by combining two results: the first one relates coverings to conjugacy of automata, and is modeled after a theorem from symbolic dynamics; the second one is an adaptation of Schützenberger's reduction algorithm of representations in a field to representations in an Euclidean domain (and thus in Z). |
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| 1 : | Laboratoire d'Informatique Gaspard-Monge (LIGM) |
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Université Paris-Est Marne-la-Vallée (UPEMLV) – ESIEE – Ecole des Ponts ParisTech – Fédération de Recherche Bézout – CNRS : UMR8049 |
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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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| 3 : | Laboratoire Traitement et Communication de l'Information [Paris] (LTCI) |
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Télécom ParisTech – CNRS : UMR5141 |
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| Domaine | : | Informatique/Mathématique discrète |
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| Automata with multiplicities – coverings of automata – conjugacy |
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| hal-00017406, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00017406 | |
| oai:hal.archives-ouvertes.fr:hal-00017406 | |
| Contributeur : Sylvain Lombardy | |
| Soumis le : Vendredi 20 Janvier 2006, 09:11:19 | |
| Dernière modification le : Vendredi 20 Janvier 2006, 09:11:19 | |
