Idempotency

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Cambridge University Press, Jan 21, 2008 - Mathematics - 456 pages
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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.
 

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Contents

An introduction to idempotency
1
Tropical semirings
50
Some automatatheoretic aspects of minmaxplus semirings
70
The finite power property for rational sets of a free group
80
The topological approach to the limitedness problem on distance automata
88
Types and dynamics in partially additive categories
112
Task resource models and max + automata
133
Algebraic system analysis of timed Petri nets
145
Maxpolynomials and discreteevent dynamic systems
282
The Stochastic HJB equation and WKB method
285
The Lagrange problem from the point of view of idempotent analysis
303
A new differential equation for the dynamics of the Pareto sets
322
Duality between probability and optimization
331
topological aspects
354
Random particle methods in max + optimization problems
383
The geometry of finite dimensional pseudomodules
392

Ergodic theorems for stochastic operators and discrete event networks
171
Computational issues in recursive stochastic systems
209
Periodic points of nonexpansive maps
231
A systemtheoretic approach for discreteevent control of manufacturing systems
242
Idempotent structures in the supervisory control of discrete event systems
262
A general linear maxplus solution technique
406
Axiomatics of thermodynamics and idempotent analysis
416
The correspondence principle for idempotent calculus and some computer applications
420
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About the author (2008)

John M. Taylor is the author a number of history books, including "Duty Faithfully Performed: Robert E. Lee and His Critics" (Brassey's, Inc., 1999). He is also a contributor to many popular history magazines including "American Heritage, Military History Quarterly", and "Civil War Times". He lives in McLean, Virginia.

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