Algebraic High-Level Nets as Weak Adhesive HLR Categories

Adhesive high-level replacement (HLR) systems have been recently introduced as a new categorical framework for double pushout transformations. Algebraic high-level nets combine algebraic specifications with Petri nets to allow the modelling of data, data flow and data changes within the net. In this paper, we show that algebraic high-level schemas and nets fit well into the context of weak adhesive HLR categories. This allows us to apply the developed theory also to algebraic high-level net transformations

Generalized Typed Attributed Graph Transformation Systems based on Morphisms Changing Type Graphs and Data Signature

Our aim is to extend the framework of typed attributed graphs in [1] to generalized typed attributed graphs. They are based on generalized attributed graph morphisms, short GAG-morphisms, which allow to change the type graph, data signature, and domain. This allows to formulate type hierarchies and views of visual languages defined by GAG-morphisms between type graphs, short GATG-morphisms. In order to study interaction and integration of views, restriction of views along type hierarchies, restriction and integration of consistent view models and reflection of behaviour between different typed attributed graph transformation systems we present suitable conditions for the construction of pushouts and pullbacks, and special van Kampen properties in the category GAGraphs of generalized attributed graphs. Moreover, we show that (GAGraphs,M) and (GAGraphsATG,M) are adhesive HLR categories for the class M of injective, persistent, and signature preserving morphisms

Negative Application Conditions for Reconfigurable Place/Transition Systems

This paper introduces negative application conditions for reconfigurable place/transition nets. These are Petri nets together with a set of rules that allow changing the net and its marking dynamically. Negative application conditions are a control structure that prohibits the application of a rule if certain structures are already existent. We motivate the use of negative application conditions in a short example. Subsequently the underlying theory is sketched and the results – concerning parallelism, concurrency and confluence – are presented. Then we resume the example and explicitly discuss the main results and their usefulness within the example

Model transformation by graph transformation: A comparative study

This is an electronic version of the paper presented at the Model Transformation in Practice, held in Montego Bay on 2005Graph transformation has been widely used for expressing model transformations. Especially transformations of visual models can be naturally formulated by graph transformations, since graphs are well suited to describe the underlying structures of models. Based on a common sample model transformation, four different model transformation approaches are presented which all perform graph transformations. At first, a basic solution is presented and crucial points of model transformations are indicated. Subsequent solutions focus mainly on the indicated problems. Finally, a first comparison of the chosen approaches to model transformation is presented where the main ingredients of each approach are summarized

Confluence of Adhesive HLR Systems with Applications to Typed Attributed Graph Transformation Systems

The concept of typed attributed graph transformation is most significant for modeling and meta modeling in software engineering and visual languages. In this thesis we introduce adhesive high-level replacement categories and systems as a new categorical frameworkforgraphtransformationinabroadsense. Itcombinesthewell-known concept of high-level replacement (HLR) systems with the new concept of adhesive categories. We show that most of the HLR properties, which had been introduced ad hoc to generalize some basic results from the category of graphs to high-level structures, are valid in adhesive HLR categories. As a main result we present a new version of embeddings and extensions for transformations in our framework of adhesive HLR systems. Moreover we show the Critical Pair Lemma for the local confluence of transformations. A new formalization of typed attributed graphs is presented, which allows node an

Graph Transformation in Adhesive HLR Categories

Abstract. In this paper we introduce the categorical framework for rule-based transformations of high-level structures, e.g. graphs, hypergraphs, typed and attributed graphs, Petri nets, etc. based on adhesive high-level replacement (HLR) categories. This generalizes the classical theory of algebraic graph transformation systems. In particular we analyze the gluing condition for transformations in a categorical way and illustrate it with an example of Petri nets.

Cospan DPO Approach: An Alternative for DPO Graph Transformations

The DPO approach for graph transformations is based on productions and direct transformations defined by two pushouts, where, roughly spoken, in the first pushout all items in L without K are deleted and in the second one all items R without K are added, while those items in K are preserved. Intuitively, K is the intersection of L and R and, formally, p is a span of graph morphisms. In this paper we consider productions which are cospans of graph morphisms, and K corresponds to the union of L and R. As before, direct transformations are defined by double pushouts, but now the first pushout adds all items in KnL and the second one deletes KnR. This basic idea can be extended to an alternative graph transformation approach, called cospan DPO approach. Key notions of the classical DPO approach can be reformulated in the cospan DPO approach and our main result shows in which way corresponding concepts and results are equivalent