Foursov, Mikhail (Univ. de Rennes-1), Hespel, Christiane (INSA de Rennes)

Weighted Petri Nets and Polynomial Dynamical Systems

Scheduled for presentation during the Regular Session "Multidimensional systems" (WeA11), Wednesday, July 26, 2006, 11:40−12:05, Room 104a

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on April 25, 2024

Abstract

In this article, we show that the generating series of polynomial dynamical systems are exactly the generating series of the subclass of weighted Petri nets where each transition has a single input place with arc weight 1. We propose furthermore an algorithm to check whether a given Petri net corresponds directly to a dynamical system. In many cases, different initial markings correspond to different dynamical systems. We finally prove that the place invariants for the Petri nets correspond to scaling Lie symmetries of the corresponding dynamical system, as well as that the invariants of the symmetry group of the dynamical system corresponds to implicit places in the corresponding Petri net.