## Methods and Applications of (max,+) Linear Algebra (1997)

Venue: | STACS'97, NUMBER 1200 IN LNCS, LUBECK |

Citations: | 75 - 26 self |

### BibTeX

@INPROCEEDINGS{Gaubert97methodsand,

author = {Stephane Gaubert and et al.},

title = {Methods and Applications of (max,+) Linear Algebra},

booktitle = {STACS'97, NUMBER 1200 IN LNCS, LUBECK},

year = {1997},

pages = {261--282},

publisher = {Springer}

}

### Years of Citing Articles

### OpenURL

### Abstract

Exotic semirings such as the "(max, +) semiring" (R # {-#},max,+), or the "tropical semiring" (N #{+#},min,+), have been invented and reinvented many times since the late fifties, in relation with various fields: performance evaluation of manufacturing systems and discrete event system theory; graph theory (path algebra) and Markov decision processes, HamiltonJacobi theory; asymptotic analysis (low temperature asymptotics in statistical physics, large deviations, WKB method); language theory (automata with multiplicities) . Despite this apparent profusion, there is a small set of common, non-naive, basic results and problems, in general not known outside the (max, +) community, which seem to be useful in most applications. The aim of this short survey paper is to present what we believe to be the minimal core of (max, +) results, and to illustrate these results by typical applications, at the frontier of language theory, control, and operations research (performance evaluation of...