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

Abstract

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