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| HAL: ensl-00507757, version 2 |
| arXiv: 1010.3685 |
| DOI: 10.1016/j.jcss.2010.08.010 |
| Detailed view |  Export this paper |
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| Journal of Computer and System Sciences 77, 4 (2011) 820-833 |
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| Available versions: | v1 (2010-07-31) | v2 (2010-10-18) |
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| The set of realizations of a max-plus linear sequence is semi-polyhedral |
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| Vincent Blondel 1Stéphane Gaubert 2, 3 |
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| (2011-07) |
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| We show that the set of realizations of a given dimension of a max-plus linear sequence is a finite union of polyhedral sets, which can be computed from any realization of the sequence. This yields an (expensive) algorithm to solve the max-plus minimal realization problem. These results are derived from general facts on rational expressions over idempotent commutative semirings: we show more generally that the set of values of the coefficients of a commutative rational expression in one letter that yield a given max-plus linear sequence is a semi-algebraic set in the max-plus sense. In particular, it is a finite union of polyhedral sets. |
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| 1: | Pôle en ingénierie mathématique (INMA) |
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Université Catholique de Louvain (UCL) - Belgique |
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| 2: | MAXPLUS (INRIA Saclay - Ile de France) |
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INRIA – CNRS : UMR – Polytechnique - X |
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| 3: | Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP) |
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Polytechnique - X – CNRS : UMR7641 |
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| 4: | Laboratoire de l'Informatique du Parallélisme (LIP) |
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Université de Lyon – CNRS : UMR5668 – INRIA – École Normale Supérieure - Lyon – Université Claude Bernard - Lyon I |
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| 5: | Department of Computer Science |
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University of Toronto |
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| Domaine | : | Computer Science/Data Structures and Algorithms Computer Science/Automatic Control Engineering |
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| max-plus algebra – minimal realization – discrete event systems – semi-polyhedral set – formal series – semiring |
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| Attached file list to this document: | ||||||||||
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| ensl-00507757, version 2 | |
| http://hal-ens-lyon.archives-ouvertes.fr/ensl-00507757 | |
| oai:hal-ens-lyon.archives-ouvertes.fr:ensl-00507757 | |
| From: Natacha Portier | |
| Submitted on: Monday, 18 October 2010 20:57:39 | |
| Updated on: Friday, 11 March 2011 16:19:37 | |
