In this paper we give a general overview of graph grammars and graph transformation as important modeling techniques for several areas in computer science. In particular we present the main ideas of the algebraic approach, which is the basis for a categorical theory of rule-based transformations of high-level structures. 1 General Overview of Graph Transformation The research area of graph gram...

In this paper, we propose a new framework of model transformation that combines graph transformation with algebraic specification. While graph transformation is well-suited to describe the transformation of visual models, one can observe that models are often composite structures with visual, graphical and diagrammatic components accompanied by all kinds of data objects like strings, sets, numb...

In this paper we define recursive rules in the double pushout approach (DPO) to graph transformation. Classical DPO rules are extended with a base case condition and a recursion condition. Mechanisms are provided to pass the match from both conditions to the rule’s left hand side, and also between two consecutive steps in the recursion. The approach is useful when recursive structures (such as ...

In the beginning, one of the main fields of application of graph transformation was biology, and more specifically morphology. Later, however, it was like if the biological applications had been left aside by the graph transformation community, just to be moved back into the mainstream these very last years with a new interest in molecular biology. In this paper, we review several fields of app...

UML is considered as the standard for object-oriented modelling language adopted by the Object Management Group. However, UML has been criticized due to the lack of formal semantics and the ambiguity of its models. In other hands, UML models can be mathematically verified and checked by using its equivalent formal representation. So, in this paper, we propose an approach and a tool based on gra...

Model transformations are central to model driven software engineering. The main aim of defining a model transformation is to reuse this model by adapting it to a new situation or context (aims of transformation include synthesis, reverse engineering, migration, optimization, refactoring, etc). Given two metamodels T1 and T2 a model transformation takes as input a model of T1 and delivers as re...

We propose an efficient implementation technique for graph transformation systems based on incremental updates. The essence of the technique is to keep track of all possible matchings of graph transformation rules in database tables, and update these tables incrementally to exploit the fact that rules typically perform only local modifications to models.

In this paper we investigate and compare four variants of the double-pushout approach to graph transformation. As well as the traditional approach with arbitrary matching and injective right-hand morphisms, we consider three variations by employing injective matching and/or arbitrary right-hand morphisms in rules. We show that injective matching provides additional expressiveness in two respect...

This report accompanies current research on membrane-inspired graph transformation systems. Contained within are details of a hypothetical model of cellular viral infection and subsequent immunological response for some imagined multicellular organism. Section 2 presents the graph transformation rules in a concrete model (after the addition of aggregating attributes) detailing the complete beha...

It is shown that it is undecidable in general whether a terminating graph rewriting system is confluent or not—in contrast to the situation for term and string rewriting systems. Critical pairs are introduced to hypergraph rewriting, a generalisation of graph rewriting, where it turns out that the mere existence of common reducts for all critical pairs of a graph rewriting system does not imply...