Graph Abstraction and Abstract Graph Transformations (Amended Version)

Many important systems such as concurrent heap-manipulating programs, communication networks, or distributed algorithms, are hard to verify due to their inherent dynamics and unboundedness. Graphs are an intuitive representation for the states of these systems, where transitions can be conveniently described by graph transformation rules. We present a framework for the abstraction of graphs supporting abstract graph transformation. The abstraction method naturally generalises previous approaches to abstract graph transformation. The set of possible abstract graphs is finite. This has the pleasant consequence of generating a finite transition system for any start graph and any finite set of transformation rules. Moreover, abstraction preserves a simple logic for expressing properties on graph nodes. The precision of the abstraction can be adjusted according to the properties expressed in this logic that are to be verified. ? The main purpose of this amended version is to correct typos, errors and omissions from previous versions of this technical report. We also tried to make the text more clear by rewriting some sentences and adding new figures. There is one major change in terminology: In the previous version of the report the term shaping was used to denote a morphism between a graph and a shape, and the term abstraction morphism to denote a morphism between two shapes. The usage of these terms were usually misleading and led to confusion. Therefore we swapped their definitions. In the current version of this report we use the term abstraction morphism to denote a morphism between a graph and a shape and we write shape morphism to indicate a morphism between two shapes.