Gunawardena J. (ed.) Idempotency

Cambridge: Cambridge University Press, 2008. — 456 p.Certain nonlinear optimization problems arise in such areas as the theory of computation, pure and applied probability, and mathematical physics. These problems can be solved through linear methods, providing the usual number system is replaced with one that satisfies the idempotent law. Only recently has a systematic study of idempotency analysis emerged, triggered in part by a workshop organized by Hewlett-Packard's Basic Research Institute in the Mathematical Sciences (BRIMS), which brought together for the first time many leading researchers in the area. This volume, a record of that workshop, includes a variety of contributions, a broad introduction to idempotency, written especially for the book, and a bibliography of the subject. It is the most up-to-date survey currently available of research in this developing area of mathematics; the articles cover both practical and more theoretical considerations, making it essential reading for all workers in the area.ForewordList of Participants
An Introduction to Idempotency
Tropical semirings.
Some automata-theoretic aspects of min-max-plus semirings
The finite power property for rational sets of a free group
The topological approach to the limitedness problem on distance automata.
Types and dynamics in partially additive categories
Task resource models and (max, +) automata
Algebraic system analysis of timed Petri nets
Ergodic theorems for stochastic operators and discrete event networks
Computational issues in recursive stochastic systems
Periodic points of nonexpansive maps
A system-theoretic approach for discrete-event control of manufacturing systems
Idempotent structures in the supervisory control of discrete event systems
Maxpolynomials and discrete-event dynamic systems
The Stochastic HJB equation and WKB method
The Lagrange problem from the point of view of idempotent analysis
A new differential equation for the dynamics of the Pareto sets
Duality between probability and optimization
Maslov optimization theory: topological aspects
Random particle methods in (max,+) optimization problems
The geometry of finite dimensional pseudomodules
A general linear max-plus solution technique
Axiomatics of thermodynamics and idempotent analysis
The correspondence principle for idempotent calculus and some computer applications