Formal Relationship between Petri Net and Graph Transformation Systems based on Functors between M-adhesive Categories

摘要

Various kinds of graph transformations and Petri net transformation systemsare examples of M-adhesive transformation systems based on M-adhesivecategories, generalizing weak adhesive HLR categories. For typed attributed graphtransformation systems, the tool environment AGG allows the modeling, the simulationand the analysis of graph transformations. A corresponding tool for Petri nettransformation systems, the RON-Environment, has recently been developed whichimplements and simulates Petri net transformations based on corresponding graphtransformations using AGG. Up to now, the correspondence between Petri net andgraph transformations is handled on an informal level. The purpose of this paper isto establish a formal relationship between the corresponding M-adhesive transformationsystems, which allow the translation of Petri net transformations into graphtransformations with equivalent behavior, and, vice versa, the creation of Petri nettransformations from graph transformations. Since this is supposed to work for differentkinds of Petri nets, we propose to define suitable functors, called M-functors,between different M-adhesive categories and to investigate properties allowing usthe translation and creation of transformations of the corresponding M-adhesivetransformation systems.