Graph transformation works under the whole world assumption. Therefore, in realistic systems, both the individual graphs and the set of all such graphs can grow very large. In reactive formalisms such as process algebra, on the other hand, each system is split into smaller components which continually interact; the interactions pass information such as names or locations between components. The...

Graph transformation systems or graph grammars are a generalization of formal grammars used in linguistics.One of principal differences is that the structures that are transformed by transformation rules are no more linear. In this paper we consider graph transformation systems in connection with proof theory. We develop the graph transformation framework, where the attributes are derivable jud...

Let H be a hexagonal system. The Z-transformation graph Z(H) is the graph where the vertices are the perfect matchings of H and where two perfect matchings are joined by an edge provided their symmetric difference is a hexagon of H (Z. Fu-ji et al., 1988). In this paper we prove that Z(H) has a Hamilton path if H is a catacondensed hexagonal system. A hexagonal system [ll], also called honeycom...

DIAPLAN is a language for programming with graphs representing diagrams that is currently being developed. The computational model of the languages, nested graph transformation, supports nested structuring of graphs, and graph variables, but is—hopefully—still intuitive. This paper is about structural typing of nested graphs and nested graph transformation systems by shape rules. We extend the ...

We present our prototypical tool for the verification of graph transformation systems. The major novelty of our tool is that it provides a model checker for temporal graph properties based on counterpart semantics for quantified μ-calculi. Our tool can be considered as an instantiation of our approach to counterpart semantics which allows for a neat handling of creation, deletion and merging in...

Graph rewriting is gaining credibility in the model transformation field, and tools are increasingly used to specify transformation activities. However, their use is often limited by special features of graph transformation approaches, which might not be familiar to experts in the modeling domain. On the other hand, transformations for specific domains may require special constraints to be enfo...

Many important systems like 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 of states of these systems, where transitions can be conveniently described by graph transformation rules. We present a framework for the abstraction of graphs supporting a...

Graph transformation systems are widely recognized as a powerful formalism for the specification of concurrent and distributed systems. Therefore, the need emerges naturally of developing formal concurrent semantics for graph transformation systems allowing for a suitable description and analysis of their computational properties. The aim of this chapter is to review and compare various concurr...