The Algebraic Approach to Performance Evaluation of Discrete Event Systems

an European Community Research Network

The algebraic approach to discrete event systems, is based on the observation that certain basic systems can be regarded as linear over suitable semirings in which the addition operation is idempotent. Surprisingly, many of the classical results of linear algebra and analysis have analogues over these idempotent semirings, giving rise to the subject of "idempotent analysis". Many of the questions rasied above can now be solved by idempotent linear techniques. However, these have not yet been applied to industrial scale problems and have not yet been incorporated in design tools for engineering use.

Idempotent analysis turns out to have important implications for a wide variety of subjects: algebric automata theory, particularly decision problems relating to distance automata; viscosity solutions of nonlinear partial differential equations, particularly the Hamilton-Jacobi-Bellman equation; optimisation theory, where an idempotent measure theory appears as the large deviation limit of classical probability theory; fixed point problems for mappings which are nonexpansive with respect to the supremum norm. These, and other, directions are under intensive investigation at the various nodes of this Research Network.

The challenge for the algebraic approach is threefold:

- Delft University of Technology, Delft, Holland

Faculty of Technical Mathematics and Informatics

Teamleader and Network Coordinator: Geert-Jan Olsder g.j.olsder@math.tudelft.nl - Ecole Nationale Supérieure des Mines de Paris,
Fontainebleau, France

Centre Automatique et Systèmes

Teamleader: Guy Cohen cohen@cas.ensmp.fr

[Synopsis of ENSMP research interests in Alapedes - INRIA Sophia-Antipolis, Sophia-Antipolis, France

Teamleader: Francois Baccelli francois.baccelli@inria.fr

INRIA Rocquencourt, Rocquencourt, France

Teamleader: Jean-Pierre Quadrat jean-pierre.quadrat@inria.fr - Catholic University of Leuven, Leuven, Belgium

Department of Electrical Engineering

Teamleader: Bart de Moor bart.demoor@esat.kuleuven.ac.be - Hewlett-Packard Laboratories, Bristol, England

Basic Research Institute in the Mathematical Sciences (BRIMS)

Teamleader: Jeremy Gunawardena jhcg@hplb.hpl.hp.com

[Synopsis of BRIMS research interests in Alapedes] - Laboratoire Informatique Théorique et Programmation

Université Pierre et Marie Curie, Paris, France

Teamleader: Daniel Krob krob@litp.ibp.fr - University of Groningen, Groningen, Holland

Research Institute of Mathematics and Computing Science

Teamleader: Reinder Smedinga rein@cs.rug.nl - Université de Liège, Liège, Belgium

Institute de Mathématique

Teamleader: Vincent Blondel blondel@math.ulg.ac.be

Geert-Jan Olsder

Delft University of Technology

Faculty of Technical mathematics and Informatics

PO Box 5031, 2600 GA Delft, Holland

`
Tel: +31 15 278 1912
Fax: +31 15 278 7209
Elm: g.j.olsder@math.tudelft.nl
`

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Last Updated: 1st May 1996.