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| HAL : hal-00270911, version 2 |
| arXiv : 0804.1092 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (07-04-2008) | v2 (29-04-2008) |
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| The special subgroup of invertible non-commutative rational power series as a metric group |
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| Roland Bacher 1 |
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| (07/04/2008) |
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| We give an easy proof of Schützenberger's Theorem stating that non-commutative formal power series are rational if and only if they are recognisable. A byproduct of this proof is a natural metric on a subgroup of invertible rational non-commutative power series. We describe a few features of this metric group. |
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| 1 : | Institut Fourier (IF) |
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CNRS : UMR5582 – Université Joseph Fourier - Grenoble I |
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| Domaine | : | Mathématiques/Combinatoire Mathématiques/Théorie des groupes |
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| non-commutative formal power series – rational series – recognisable series – metric group – automaton sequence – regular language |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00270911, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00270911 | |
| oai:hal.archives-ouvertes.fr:hal-00270911 | |
| Contributeur : Roland Bacher | |
| Soumis le : Mardi 29 Avril 2008, 13:36:39 | |
| Dernière modification le : Mardi 29 Avril 2008, 13:53:06 | |
