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| HAL: hal-00458295, version 1 |
| arXiv: 1002.3866 |
| Detailed view |  Export this paper |
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| Available versions: | v1 (2010-02-20) | v2 (2011-02-04) | v3 (2011-03-04) |
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| Deciding the finiteness of the number of simple permutations contained in a wreath-closed class is polynomial |
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Frédérique Bassino 1Mathilde Bouvel 2 |
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| (2010-02-15) |
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| We present an algorithm running in time O(n ln n) which decides if a wreath-closed permutation class Av(B) given by its finite basis B contains a finite number of simple permutations. The method we use is based on an article of Brignall, Ruskuc and Vatter which presents a decision procedure (of high complexity) for solving this question, without the assumption that Av(B) is wreath-closed. Using combinatorial, algorithmic and language theoretic arguments together with one of our previous results on pin-permutations, we are able to transform the problem into a co-finiteness problem in a complete deterministic automaton. |
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| 1: | Laboratoire d'informatique de Paris-nord (LIPN) |
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CNRS : UMR7030 – Université Paris XIII - Paris Nord |
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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 d'informatique de l'école polytechnique (LIX) |
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CNRS : UMR7161 – Polytechnique - X |
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| Subject | : | Computer Science/Data Structures and Algorithms Mathematics/Combinatorics |
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| hal-00458295, version 1 | |
| http://hal-polytechnique.archives-ouvertes.fr/hal-00458295 | |
| oai:hal-polytechnique.archives-ouvertes.fr:hal-00458295 | |
| From: Dominique Rossin | |
| Submitted on: Friday, 19 February 2010 22:17:23 | |
| Updated on: Saturday, 20 February 2010 11:54:07 | |
