Comparison of incidence matrices to detect common patterns in petri nets

Resumen

Given a discrete event system modeled by an alternatives Petri net system, the identification of common patterns is required in the incidence matrices in order to transform the model into another minimum one necessary to develop a more efficient optimization. Transformations of set of the alternatives Petri nets to be considered are two: Aggregation and fusion. Aggregation is used to obtain alternatives Petri nets, and is performed by means of the following operations: identifying of shared subnets on the alternative nets, identification of binding transitions and unshared blocks, and aggregation of the incidence matrices. Fusion is used for obtaining a composed Petri net, and is made by means of the following operations: Application of swaps to rows or columns to achieve an optimal configuration, and overlay of matrices. Those types of transformations on Petri nets are based on the equivalence class of the incidence matrices that can be formed by permuting or swapping the rows and the columns. This paper constitutes such a basis, by means of the analysis of this equivalence class. © 2013 DIME UNIVERSITÀ DI GENOVA.