In: Gianfranco Ciardo, Philippe Darondeau (Eds.): Lecture Notes in Computer Science, Vol. 3536: Applications and Theory of Petri Nets 2005: 26th International Conference, ICATPN 2005, Miami, USA, June 20-25, 2005., pages 26-47. Springer Verlag, June 2005.
Abstract: State explosion is a fundamental problem in the analysis and synthesis of discrete event systems. Continuous Petri nets can be seen as a relaxation of discrete models allowing more efficient (in some cases polynomial time) analysis and synthesis algorithms. Nevertheless computational costs can be reduced at the expense of the analyzability of some properties. Even more, some net systems do not allow any kind of continuization. The present work first considers these aspects and some of the alternative formalisms usable for continuous relaxations of discrete systems. Particular emphasis is done later on the presentation of some results concerning performance evaluation, parametric design and marking (i.e., state) observation and control. Even if a significant amount of results are available today for continuous net systems, many essential issues are still not solved. A list of some of these are given in the introduction as an invitation to work on them.