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
收藏
页码：820 / 833
页数：14
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