Idempotency

A survey of idempotency, the developing area of mathematics.

Jeremy Gunawardena (Edited by), John M. Taylor (Foreword by), Michael Atiyah (Foreword by)

9780521553445, Cambridge University Press

Hardback, published 13 January 1998

456 pages, 25 b/w illus.
23.5 x 15.9 x 3.1 cm, 0.84 kg

'… essential reading for everybody interested in the area.' European Mathematical Society

Certain nonlinear optimization problems arising in such disparate areas as the theory of computation, pure and applied probability and mathematical physics, can be solved by linear methods, provided one replaces the usual number system with one in which addition satisfies the idempotent law. This systematic study of the subject has emerged, triggered in part by a workshop organized by Hewlett-Packard's Basic Research Institute in the Mathematical Sciences (BRIMS), which brought together many leading researchers in the area. This volume is a record of that workshop, but it also includes other invited contributions, a broad Introduction to Idempotency, written specially for the book, and a bibliography of the subject. In sum, the articles cover both practical and more theoretical considerations, making it essential reading for all workers in the area.

Foreword
Preface
List of participants
1. An introduction to idempotency Jeremy Gunawardena
2. Tropical semirings Jean-Eric Pin
3. Some automata-theoretic aspects of min-max-plus semirings Daniel Krob
4. The finite power property for rational sets of a free group Flavio d'Alessandro and Jacques Sakarovitch
5. The topological approach to the limitedness problem on distance automata Hing Leung
6. Types and dynamics in partially additive categories Gianfranco Mascari and Marco Pedicini
7. Task resource models and (max,+) automata Stéphane Gaubert and Jean Mairesse
8. Algebraic system analysis of timed Petri nets Guy Cohen, Stéphane Gaubert and Jean-Pierre Quadrat
9. Ergodic theorems for stochastic operators and discrete event networks François Baccelli and Jean Mairesse
10. Computational issues in recursive stochastic systems Bruno Gaujal and Alain Jean-Marie
11. Periodic points of nonexpansive maps Roger D. Nussbaum
12. A system-theoretic approach for discrete-event control of manufacturing systems Ayla Gürel, Octavian C. Pastravanu and Frank L. Lewis
13. Idempotent structures in the supervisory control of discrete event systems Darren D. Cofer and Vijay K. Garg
14. Maxpolynomials and discrete-event dynamic systems Raymond A. Cunninghame-Green
15. The Stochastic HJB equation and WKB method Vassili N. Kolokoltsov
16. The Lagrange problem from the point of view of idempotent analysis Serguei Samborskii
17. A new differential equation for the dynamics of the Pareto sets Vassili N. Kolokoltsov and Victor P. Maslov
18. Duality between probability and optimization Marianne Akian, Jean-Pierre Quadrat and Michel Viot
19. Maslov optimization theory: topological aspects Pierre Del Moral
20. Random particle methods in (max,+) optimization problems Pierre Del Moral and Gérard Salut
21. The geometry of finite dimensional pseudomodules Edouard Wagneur
22. A general linear max-plus solution technique Elizabeth A. Walkup and Gaetano Borriello
23. Axiomatics of thermodynamics and idempotent analysis Victor P. Maslov
24. The correspondence principle for idempotent calculus and some computer applications Grigori L. Litvinov and Victor P. Maslov.

Subject Areas: Applied mathematics [PBW]