Analysis of Hypergraph Transformation Systems in AGG based on M-Functors

Abstract

Hypergraph transformation systems are examples of M-adhesive transformation systems based on M-adhesive categories. For typed attributed graph transformation systems, the tool environment AGG allows the modelling, the simu-
lation and the analysis of graph transformations. A corresponding tool for analysis of hypergraph transformation systems does not exist up to now. The purpose of this paper is to establish a formal relationship between the corresponding M-adhesive transformation systems, which allows us the translation of hypergraph transformations into typed attributed graph transformations with equivalent behavior, and, vice versa, the creation of hypergraph transformations from typed attributed graph transformations. This formal relationship is based on the general theory of M-functors between different M-adhesive transformation systems. We construct a functor between the M-adhesive categories of hypergraphs and of typed attributed graphs, and show that our construction yields an M-functor with suitable properties. We then use existing results for M-functors to show that analysis results for hypergraph transformation systems can be obtained using AGG  by analysis of the translated typed attributed graph transformation system. This is shown in general and for a concrete example.