Local confluence analysis of hypergraph transformation systems with application conditions based on MM-functors and Agg

–We translate hypergraph transformations to typed attributed graph transformations.–We use MM-functors between MM-adhesive categories for the translation.–We show that MM-functors translate and create local confluence (critical pairs).–We extend these results to rules with general (nested) application conditions.–Hence, we can apply the tool Agg to analyze hypergraph transformation systems.

For typed attributed graph transformation systems, the tool environment Agg supports modelling, simulation and analysis of graph transformations. A corresponding tool for analysis of hypergraph transformation systems does not exist up to now. In this paper we establish a formal relationship between the corresponding MM-adhesive transformation systems, which allows us the translation of hypergraph transformations into typed attributed graph transformations with equivalent behaviour, and, vice versa, the creation of hypergraph transformations from typed attributed graph transformations. This relationship is based on the general theory of MM-functors between different MM-adhesive transformation systems which is extended in this paper to rules with application conditions. Our main result shows the creation of local confluence based on FF-reachable critical pairs for rules with application conditions, where FF is a suitable MM-functor. We construct a functor between the MM-adhesive categories of hypergraphs and of typed attributed graphs, and show that our construction yields an MM-functor with properties required by the general theory. Hence, analysis results for hypergraph transformation systems can be obtained using Agg for analysing the translated typed attributed graph transformation systems.