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.
Author(s): Jeremy Gunawardena, John M. Taylor, Michael Atiyah
Series: Publications of the Newton Institute
Edition: 1
Publisher: Cambridge University Press
Year: 2008
Language: English
Pages: 456
Cover......Page 1
Title......Page 4
Copyright......Page 5
Contents ......Page 6
Foreword ......Page 8
Preface ......Page 10
List of Participants ......Page 12
An Introduction to Idempotency......Page 14
Tropical semirings ......Page 63
Some automata-theoretic aspects of min-max-plus semirings ......Page 83
The finite power property for rational sets of a free group ......Page 93
The topological approach to the limitedness problem on distance automata ......Page 101
Types and dynamics in partially additive categories ......Page 125
Task resource models and (max, +) automata ......Page 146
Algebraic system analysis of timed Petri nets ......Page 158
Ergodic theorems for stochastic operators and discrete event networks. ......Page 184
Computational issues in recursive stochastic systems ......Page 222
Periodic points of nonexpansive maps ......Page 244
A system-theoretic approach for discrete-event control of manufacturing systems ......Page 255
Idempotent structures in the supervisory control of discrete event systems ......Page 275
Maxpolynomials and discrete-event dynamic systems ......Page 295
The Stochastic HJB equation and WKB method ......Page 298
The Lagrange problem from the point of view of idempotent analysis ......Page 316
A new differential equation for the dynamics of the Pareto sets ......Page 335
Duality between probability and optimization ......Page 344
Maslov optimization theory: topological aspects ......Page 367
Random particle methods in (max,+) optimization problems ......Page 396
The geometry of finite dimensional pseudomodules ......Page 405
A general linear max-plus solution technique ......Page 419
Axiomatics of thermodynamics and idempotent analysis ......Page 429
The correspondence principle for idempotent calculus and some computer applications ......Page 433
