The set of realizations of a max-plus linear sequence is semi-polyhedral

被引：1

作者：

Blondel, Vincent ^{[2
]}

Gaubert, Stephane ^{[3
,4
]}

Portier, Natacha ^{[1
,5
]}

机构：

[1] Univ Lyon, LIP, Ecole Normale Super Lyon, CNRS,UCBL,INRIA,ENS Lyon,UMR 5668, F-69364 Lyon 07, France

[2] Catholic Univ Louvain, Dept Ingn Math, Large Graphs & Networks, B-1348 Louvain, Belgium

[3] Ecole Polytech, CMAP, F-91128 Palaiseau, France

[4] Ecole Polytech, INRIA, F-91128 Palaiseau, France

[5] Univ Toronto, Dept Comp Sci, Toronto, ON M5S 1A1, Canada

来源：

JOURNAL OF COMPUTER AND SYSTEM SCIENCES | 2011年 / 77卷 / 04期

关键词：

Max-plus algebra; Minimal realization; Discrete event systems; Semi-polyhedral set; Formal series; Semiring; DISCRETE-EVENT SYSTEMS; PERFORMANCE EVALUATION; DYNAMIC-SYSTEMS; GEOMETRY;

D O I：

10.1016/j.jcss.2010.08.010

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

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 finite union of polyhedral sets. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：820 / 833

页数：14

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