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Journal articles
The set of realizations of a max-plus linear sequence is semi-polyhedral
Abstract : 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.
Cited literature [46 references]
https://hal-ens-lyon.archives-ouvertes.fr/ensl-00507757
Contributor : Natacha Portier <>
Submitted on : Monday, October 18, 2010 - 8:57:39 PM
Last modification on : Thursday, March 5, 2020 - 6:23:39 PM
Long-term archiving on: : Wednesday, January 19, 2011 - 2:55:41 AM
Contributor : Natacha Portier <>
Submitted on : Monday, October 18, 2010 - 8:57:39 PM
Last modification on : Thursday, March 5, 2020 - 6:23:39 PM
Long-term archiving on: : Wednesday, January 19, 2011 - 2:55:41 AM
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