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...

• Type: Conference
• Year: 1997
• Where: STACS
• Authors: Stephane Gaubert, Max Plus
• Keywords: Language Theory, Low Temperature Asymptotics, Markov Decision, STACS 1997, Theoretical Computer Science