On rational series in one variable over certain dioids

Abstract : We give a characterization of rational series in one variable over certain idempotent semirings (commutative dioids) such as for instance the ``$(\max,+)$ ''semiring. We show that a series is rational iff it is merge of ultimately geometric series. As a by-product, we obtain a new proof of the periodicity theorem for powers of irreducible matrices and also some more general auxiliary results. We apply this characterization of rational series to the minimal realization problem for which we obtain an upper bound. We also obtain a lower bound in terms of minors in a symmetrized semiring
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Rapport
[Research Report] RR-2162, INRIA. 1994
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https://hal.inria.fr/inria-00074510
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Soumis le : mercredi 24 mai 2006 - 15:34:23
Dernière modification le : vendredi 25 mai 2018 - 12:02:05
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Stéphane Gaubert. On rational series in one variable over certain dioids. [Research Report] RR-2162, INRIA. 1994. 〈inria-00074510〉

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