Petri net reduction rules through incidence matrix operations

A Petri net (PN) is a powerful tool that has been used tomodel and analyze discrete event systems. Suchsystems can be concurrent, asynchronous, distributed,parallel, non-deterministic, and/or stochastic. A problemin PN modelling is related to its graphicalrepresentation because it increases for each element ofthe system. Consequently, incidence matrix of the PNalso increases the number of rows and/or columns. Toverify properties in PN such as liveness, safeness, andboundedness, computer time is required, even more ifwe need to verify huge Petri nets. There are six simplereduction rules, which are used to produce a smaller PNpreserving the properties of the original PN. In order toapply these reduction rules, we have to find the patternand then apply the corresponding rule. In this paper, wepropose to apply the reduction rules directly in theincidence matrix of the PN modelled, detecting thepattern of each rule on the incidence matrix andapplying the corresponding changes on the incidencematrix.