Transfer of Local Confluence and Termination between Petri Net and Graph Transformation Systems Based on M -Functors

Abstract

Recently, a formal relationship between Petri net and graph transforma- tion systems has been established using the new framework of M -functors F : (C1;M1)! (C2;M2) between M -adhesive categories. This new approach al- lows to translate transformations in (C1;M1) into corresponding transformations in (C2;M2) and, vice versa, to create transformations in (C1;M1) from those in (C2;M2). This is helpful because our tool for reconfigurable Petri nets, the RON- tool, performs the analysis of Petri net transformations by analyzing corresponding graph transformations using the AGG-tool. Up to now, this correspondence has been implemented as a converter on an informal level. The formal correspondence results given by our framework make the RON-tool more reliable. In this paper we extend this framework to the transfer of local confluence, termination and func- tional behavior. In particular, we are able to create these properties for transforma- tions in (C1;M1) from corresponding properties of transformations in (C2;M2), where (C1;M1) are Petri nets with individual tokens and (C2;M2) typed attributed graphs. This allows us to apply the well-known critical pair analysis for typed at- tributed graph transformations supported by the AGG-tool in order to analyze these properties for Petri net transformations.