Application of Graph Transformation Techniques to the Area of Petri Nets: An Overview

The main aim of this contribution is to give an overview concerning applications of graph transformation techniques to the area of Petri nets achieved by the team of TU Berlin within the APPLIGRAPH Working Group and the DFG Researcher Group on Petri Net Technology. Since about 10 years the strong relationships between the areas of Petri nets and graph transformation systems have been studied especially as part of the cooperation of the groups in Pisa and Berlin, while it was observed by Kreowski already in the early 80s how Petri nets can be considered as a special case of graph transformation systems. The main aim of the Pisa-Berlin cooperation was to transfer the well-known constructions leading to a truly concurrent event structure semantics from Petri nets to graph transformation systems. Vice versa the concept of high-level replacement systems, short HLR-systems, by Ehrig, Habel, Kreowski and Parisi-Presicce in [EHKP91] was the starting point to obtain new concepts and results for the area of Petri nets by application of graph transformation techniques. In fact the concept of HLR-systems in [EHKP91] is a generalization of the double pushout approach from graph transformation to HLR-systems in a categorical framework. The instantiation of HLR-systems to Petri nets leads to the concept of net transformation systems [PER95], which will be discussed in Section 2. In order to study property preserving transformations, the concept of HLR-transformations was extended by Padberg in [Pad96] to Q-transformations leading to safety and liveness preserving transformations in [PGE98,GHP99] and [GPU01] respectively reviewed in Section 3. In Section 4 we discuss in which way the module concept for graph transformation systems developed by Simeoni [Sim00] has been transferred to Petri nets [PHBS02] and to a generic component concept in [EOBKP02]. In Section 5 we discuss the modeling of open systems, where the