HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Reports

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
Document type :
Reports
Complete list of metadata

https://hal.inria.fr/inria-00074510
Contributor : Rapport de Recherche Inria Connect in order to contact the contributor
Submitted on : Wednesday, May 24, 2006 - 3:34:23 PM
Last modification on : Thursday, February 3, 2022 - 11:17:20 AM
Long-term archiving on: : Sunday, April 4, 2010 - 10:18:48 PM

Identifiers

  • HAL Id : inria-00074510, version 1

Collections

Citation

Stéphane Gaubert. On rational series in one variable over certain dioids. [Research Report] RR-2162, INRIA. 1994. ⟨inria-00074510⟩

Share

Metrics

Record views

74

Files downloads

127