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...

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...

We present conditions under which graph transformation rules can be applied in time independent of the size of the input graph: graphs must contain a unique root label, nodes in the left-hand sides of rules must be reachable from the root, and nodes must have a bounded outdegree. We establish a constant upper bound for the time needed to construct all graphs resulting from an application of a f...

Modern software systems increasingly incorporate self-* behavior to adapt to changes in the environment at runtime. Such adaptations often involve reconfiguring the software architecture of the system. Many systems also need to manage their architecture themselves, i.e., they need a planning component to autonomously decide which reconfigurations to execute to reach a desired target configurati...

We describe a tool to create, edit, visualise and compute with interaction nets — a form of graph rewriting systems. The editor, called GraphPaper, allows users to create and edit graphs and their transformation rules using an intuitive user interface. The editor uses the functionalities of the TULIP system, which gives us access to a wealth of visualisation algorithms. Interaction nets are not...

The development of a denotational framework for graph transformation systems proved elusive so far. Despite the existence of many formalisms for modelling various notions of rewriting, the lack of an explicit, algebraic notion of “term” for describing a graph (thus different from the usual view of a graph as an algebra in itself) frustrated the efforts of the researchers. Resorting to the theor...

Graph transformation can be used to implement stochastic simulation of dynamic systems based on semi-Markov processes, extending the standard approach based on Markov chains. The result is a discrete event system, where states are graphs, and events are rule matches associated to general distributions, rather than just exponential ones. We present an extension of this model, by introducing a hi...

This document provides insight to the similarities and differences of Graph Transformation and AI Planning, two rising research fields with different publication organs and tools. While graph transformation systems can be used as a graphical knowledge engineering front-end for designing planning problems, AI planning technology (especially heuristic search) can accelerate the exploration proces...

We consider a graph with labels of edges. A label means the length of an edge. We present a method to compute the length of the shortest path between two vertices using graph transformations. We introduce graph transformation rules which preserve the length of paths. Reducing to a simple graph which contains two vertices, we finally calculate the length of the shortest path of those two vertice...