Methods and Applications of (MAX, +) Linear Algebra

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Methods and Applications of (MAX, +) Linear Algebra
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:performanceevaluationofmanufacturingsystemsanddiscreteeventsystem 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 eval...
Stephane Gaubert, Max Plus
Added 08 Aug 2010
Updated 08 Aug 2010
Type Conference
Year 1997
Authors Stephane Gaubert, Max Plus
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