Semantical Correctness and Completeness of Model Transformations using Graph and Rule Transformation: Long Version

An important requirement of model transformations is the preservation of the behavior of the original model. A model transformation is semantically correct if for each simulation run of the source system we find a corresponding simulation run in the target system. Analogously, we have semantical completeness, if for each simulation run of the target system we find a corresponding simulation run in the source system. In our framework of graph transformation, models are given by graphs, and graph transformation rules are used to define the operational behavior of visual models (called simulation rules). In order to compare the semantics of source and target models, we assume that in both cases operational behavior can be defined by simulation rules. The model transformation from source to target models is given by another set of graph transformation rules. These rules are also applied to the simulation rules of the source model. The result of this rule transformation is compared with the given simulation rules of the target language.The main result in this paper states the conditions for model and rule transformations to be semantically correct and complete. The result is applied to analyze the behavior of a model transformation from a domain-specific visual language for production systems to Petri nets

Preface

Preface of the Proceedings of the Fourth International Workshop on Petri Nets and Graph Transformation PNGT 201

Graph Modelling and Transformation: Theory meets Practice

In this paper, we focus on the role of graphs and graph transformation for four practical application areas from software system development. We present the typical problems in these areas and investigate how the respective systems are modelled by graphs and graph transformation. In particular, we are interested in the usefulness of theoretical graph transformation results and graph transformation tools in order to solve these problems. Finally, we characterize concepts and tool features which are still missing in practice to solve the presented and related problems even better. Keywords: graph modelling, graph transformation, graph transformation tool

Parallel Graph Transformation for Model Simulation applied to Timed Transition Petri Nets

Proceedings of the Workshop on Graph Transformation and Visual Modelling Techniques (GT-VMT 2004)This work discusses the use of parallel graph transformation systems for (multi-formalism) modeling and simulation and their implementation in the meta-modeling tool AToM3. As an example, a simulator for Timed Transition Petri Nets (TTPN) is modeled using parallel graph transformation.This work has been partially sponsored by the SEGRAVIS network and the Spanish Ministry of Science and Technology (TIC2002-01948)

Semantical Correctness of Simulation-to-Animation Model and Rule Transformation

In the framework of graph transformation, simulation rules are well-known to define the operational behavior of visual models. Moreover, it has been shown already how to construct animation rules in a domain specific layout from simulation rules. An important requirement of this construction is the semantical correctness which has not yet been considered. In this paper we give a precise definition for simulation-to-animation (S2A) model and rule transformations. Our main results show under which conditions semantical correctness can be obtained. The results are applied to analyze the S2A transformation of a Radio Clock model. Keywords: graph transformation, model and rule transformation, semantical correctness, simulation, animatio

Refactoring of Model Transformations

Model-to-model transformations between visual languages are often defined by typed, attributed graph transformation systems. Here, the source and target languages of the model transformation are given by type graphs (or meta models), and the relation between source and target model elements is captured by graph transformation rules. On the other hand, refactoring is a technique to improve the structure of a model in order to make it easier to comprehend, more maintainable and amenable to change. Refactoring can be defined by graph transformation rules, too. In the context of model transformation, problems arise when models of the source language of a model transformation become subject to refactoring. It may well be the case that after the refactoring, the model transformation rules are no longer applicable because the refactoring induced structural changes in the models. In this paper, we consider a graph-transformation-based evolution of model transformations which adapts the model transformation rules to the refactored models. In the main result, we show that under suitable assumptions, the evolution leads to an adapted model transformation which is compatible with refactoring of the source and target models. In a small case study, we apply our techniques to a well-known model transformation from statecharts to Petri nets

Algebraic Approach to Timed Petri Nets

One aspect often needed when modelling systems of any kind is time-based analysis, especially for real-time or in general time-critical systems. Algebraic place/transition (P/T) nets do not inherently provide a way to model the passing of time or to restrict the firing behaviour with regards to passing time. In this paper, we present an extension of algebraic P/T nets by adding time durations to transitions and timestamps to tokens. We define categories for different timed net classes and functorial relations between them. Our first result is the definition of morphisms preserving firing behaviour for all timed net classes. As second result, we define structuring techniques for timed P/T nets in a way that our category fulfills the properties of M-adhesive systems, a general categorical framework for structuring and transforming high-level algebraic structures. We demonstrate our approach by applying it to model a real-time communication network

Functors between M-adhesive Categories Applied to Petri Net and Graph Transformation Systems

Various kinds of graph transformations and Petri net transformation systems are examples of M-adhesive transformation systems based on M-adhesive categories, generalizing weak adhesive HLR categories. For typed attributed graph transformation systems, the tool environment AGG allows the modeling, the simulation and the analysis of graph transformations. A corresponding tool for Petri net transformation systems, the RON-Environment, has recently been developed which implements and simulates Petri net transformations based on corresponding graph transformations using AGG. Up to now, the correspondence between Petri net and graph transformations is handled on an informal level. The purpose of this paper is to establish a formal relationship between the corresponding M-adhesive transformation systems, which allow the translation of Petri net transformations into graph transformations with equivalent behavior, and, vice versa, the creation of Petri net transformations from graph transformations. Since this is supposed to work for different kinds of Petri nets, we propose to define suitable functors, called M-functors, between different M-adhesive categories and to investigate properties allowing us the translation and creation of transformations of the corresponding M-adhesive transformation systems

A Formal Resolution Strategy for Operation-Based Conicts in Model Versioning Using Graph Modications

In model-driven engineering, models are primary artifacts and can evolve heavily during their life cycle. Hence, versioning of models is a key technique which has to be offered by an integrated development environment for model-driven engineering. In contrast to textbased versioning systems, our approach takes abstract syntax structures in model states and operational features into account. Considering the abstract syntax of models as graphs, we define a model revision by a span G H, called graph modification, where G and H are the old and new versions, respectively, and D the common subgraph that remains unchanged. Based on notions of behavioural equivalence and parallel independence of graph modifications, we are able to show a Local-Church- Rosser Theorem for graph modifications. The main goal of the paper is to handle conflicts of graph modifications which may occur in the case of parallel dependent graph modifications. The main result is a general merge construction for graph modifications that resolves all conflicts simultaneously in the sense that for delete-insert conflicts insertion has priority over deletion

Analysis of Hypergraph Transformation Systems in AGG based on M-Functors: Extended Version

Hypergraph transformation systems are examples ofM-adhesive transformation systems based on M-adhesive categories. For typed attributed graph transformation systems, the tool environment Agg allows the modelling, the simulation and the analysis of graph transformations. A corresponding tool for analysis of hypergraph transformation systems does not exist up to now. The purpose of this paper is to establish a formal relationship between the corresponding M- adhesive transformation systems, which allows us the translation of hypergraph transformations into typed attributed graph transformations with equivalent behavior, and, vice versa, the creation of hypergraph transformations from typed attributed graph transformations. This formal relationship is based on the general theory ofM-functors between differentM-adhesive transformation systems. We construct a functor between the M-adhesive categories of hypergraphs and of typed attributed graphs, and show that our construction yields an M-functor with suitable properties. We then use existing results for M-functors to show that analysis results for hypergraph transformation systems can be obtained using Agg by analysis of the translated typed attributed graph transformation system. This is shown in general and for a concrete example