Branching Processes of General Petri Nets

Abstract

We propose a new model of branching processes, suitable for describing the behavior of general Petri nets, without any finiteness or safeness assumption. In this framework, we define a new class of branching processes and unfoldings of a net N, which we call true. These coincide with the safe branching processes and unfoldings if N is safe, or weakly safe as in [Engelfriet 1991], but not in general. However, true branching processes and processes satisfy the good order-theoretic properties which make the safe processes of safe nets so useful in practice, and which are known not to hold for the safe processes of a general net. True processes represent therefore good candidates to generalize the theory of safe nets to the general case.

This paper was prepared in part while the first author was on a 2-year assignment at LSV (ENS Cachan) with the support of CNRS. The third author acknowledges partial support from Project versydis, ACI Sécurité informatique, Ministère de l’Industrie.