Language, Liveness and Fairness Invariant in Decomposition of Petri Net Based on the Index of Place

Abstract

It is not easy to analyze the physical system with Petri net if the system is large-scaled and complex, mainly because the structure of the Petri net model is also complex. In order to overcome this difficulty, a decomposition method of Petri net based on an index function of places is introduced, with which a set of well-formed and structure-simple sub net systems can be obtained. For all the sub net systems, the number of all the input or output places of each transition is less than or equal to one. The relationships about the reachable states, languages, liveness and fairness between the original Petri net and its sub net systems are analyzed with details. The sufficient and necessary conditions are presented to keep the reachable states and languages invariant during the decomposition process, which is useful for analysis of liveness and fairness of structure-complex Petri net systems.