In this paper, we give an overview of the framework of graph transformation units which provides syntactic and semantic means for analyzing, modeling, and structuring all kinds of graph processing and graph transformation.

This chapter introduces rule-based graph transformation, which constitutes a well-studied research area in computer science. The chapter presents the most fundamental definitions and illustrates them with some selected examples. It presents also the concept of transformation units, which makes pure graph transformation more feasible for specification and modeling aspects. Moreover, a translatio...

Impressum Forschungsberichte der FHDW Hannover – Veröffentlichungen aus dem Bereich Forschung und Entwicklung der FHDW Hannover. Abstract. The paper extends single-pushout graph transformation by poly-morphism, a key concept in object-oriented design. The notions sub-rule and remainder, well-known in single-pushout rewriting, are applied to model dynamic rule extension and type dependent rule a...

We review the concept of term graph narrowing as an approach for solving equations by transformations on term graphs. Term graph narrowing combines term graph rewriting with rst-order term uni cation. This mechanism is complete for all term rewriting systems over which term graph rewriting is normalizing and conuent. This includes, in particular, all convergent term rewriting systems. Completen...

We present a novel approach to implement a graph transformation engine based on standard relational database management systems (RDBMSs). The essence of the approach is to create database views for each rules and to handle pattern matching by inner join operations while negative application conditions by left outer join operations. Furthermore, the model manipulation prescribed by the applicati...

We establish a machine-checkable condition which ensures that the union of two terminating hypergraph transformation systems is terminating. The condition is based on so-called sequential critical pairs which represent consecutive rule applications that are not independent. In contrast to a corresponding modularity result for term rewriting, no restrictions on the form of rules are required. Ou...

We present a notion of composition applying both to graphs and to rules, based on graph and rule interfaces along which they are glued. The current paper generalises a previous result in two different ways. Firstly, rules do not have to form pullbacks with their interfaces; this enables graph passing between components, meaning that components may “learn” and “forget” subgraphs through communic...

Even sophisticated techniques start out from simple ideas. Later, in reply to application needs or theoretical problems new concepts are introduced and new formalizations proposed, often to a point where the original simple core is hardly recognizable. In this paper we provide a non-technical introduction to the basic concepts of typed graph transformation systems, completed with a survey of mo...

In this paper we present meta-rules to express an infinite class of semantically related graph transformation rules in the context of pure topological modelling with G-maps. Our proposal is motivated by the need of describing specific operations to be done on topological representations of objects in computer graphics, especially for simulation of complex structured systems where rearrangements...

We believe that the technique of graph transformation offers a very natural way to specify semantics for languages that have dynamic allocation and linking structure; for instance, object-oriented programming languages, but also languages for mobility. In this note we expose, on a rather informal level, the reasons for this belief. Our hope in doing this is to raise interest in this technique a...