Petri net reduction rules through incidence matrix operations

Abstract

A Petri net (PN) is a powerful tool that has been used to model and analyze discrete event systems. Such systems can be concurrent, asynchronous, distributed, parallel, non-deterministic, and/or stochastic. A problem in PN modelling is related to its graphical representation because it increases for each element of the system. Consequently, incidence matrix of the PN also increases the number of rows and/or columns. To verify properties in PN such as liveness, safeness, and boundedness, computer time is required, even more if we need to verify huge Petri nets. There are six simple reduction rules, which are used to produce a smaller PN preserving the properties of the original PN. In order to apply these reduction rules, we have to find the pattern and then apply the corresponding rule. In this paper, we propose to apply the reduction rules directly in the incidence matrix of the PN modelled, detecting the pattern of each rule on the incidence matrix and applying the corresponding changes on the incidence matrix.