Attributed Graph Transformation Systems Research Articles

Stochastic Graph Transformation For Social Network Modeling

Adaptive networks model social, physical, technical, or biological systems as attributed graphs evolving at the level of both their topology and data. They are naturally described by graph transformation, but the majority of authors take an approach inspired by the physical sciences, combining an informal description of the operations with programmed simulations, and systems of ODEs as the only abstract mathematical description. We show that we can capture a range of social network models, the so-called voter models, as stochastic attributed graph transformation systems, demonstrate the benefits of this representation and establish its relation to the non-standard probabilistic view adopted in the literature. We use the theory and tools of graph transformation to analyze and simulate the models and propose a new variant of a standard stochastic simulation algorithm to recreate the results observed.

Local confluence analysis of hypergraph transformation systems with application conditions based on [formula omitted]-functors and Agg

For typed attributed graph transformation systems, the tool environment Agg supports modelling, simulation and analysis of graph transformations. A corresponding tool for analysis of hypergraph transformation systems does not exist up to now. In this paper we 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 behaviour, and, vice versa, the creation of hypergraph transformations from typed attributed graph transformations. This relationship is based on the general theory of M-functors between different M-adhesive transformation systems which is extended in this paper to rules with application conditions. Our main result shows the creation of local confluence based on F-reachable critical pairs for rules with application conditions, where F is a suitable M-functor. 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 properties required by the general theory. Hence, analysis results for hypergraph transformation systems can be obtained using Agg for analysing the translated typed attributed graph transformation systems.

Formal analysis of model transformations based on triple graph grammars

Triple graph grammars (TGGs) are a well-established concept for the specification and execution of bidirectional model transformations within model driven software engineering. Their main advantage is an automatic generation of operational rules for forward and backward model transformations, which simplifies specification and enhances usability as well as consistency. In this paper we present several important results for analysing model transformations based on the formal categorical foundation of TGGs within the framework of attributed graph transformation systems.Our first main result shows that the crucial properties of correctness and completeness are ensured for model transformations. In order to analyse functional behaviour, we generate a new kind of operational rule, called aforward translation rule. We apply existing results for the analysis of local confluence for attributed graph transformation systems. As additional main results, we provide sufficient criteria for the verification of functional behaviour as well as a necessary and sufficient condition for strong functional behaviour. In fact, these conditions imply polynomial complexity for the execution of the model transformation. We also analyse information and complete information preservation of model transformations, that is, whether a source model can be reconstructed (uniquely) from the target model computed by the model transformation. We illustrate the results for the well-known model transformation example from class diagrams to relational database models.

Overview of Formal Concepts for Model Transformations Based on Typed Attributed Graph Transformation

In this paper we give an overview of formal concepts for model transformations between visual languages based on typed attributed graph transformation. We start with a basic concept where visual languages are defined by attributed type graphs only and model transformations by basic typed attributed graph transformation systems. We continue with different kinds of extensions of the basic concepts taking into account application conditions, constraints, generating graph grammars and operational semantics. The main aim is to discuss formal correctness criteria for model transformations including syntactical correctness, functional behavior and semantical correctness.

High-level replacement units and their termination properties

Visual rewriting techniques, in particular graph transformations, are increasingly used to model transformations of systems specified through diagrammatic sentences. Several rewriting models have been proposed, differing in the expressivity of the types of rules and in the complexity of the rewriting mechanism; yet, for many of them, basic results concerning the formal properties of these models are still missing. In this paper, we give a contribution towards solving the termination problem for rewriting systems with external control mechanisms. In particular, we obtain results of more general validity by extending the concept of transformation unit to high-level replacement systems, a generalization of graph transformation systems. For high-level replacement units, we state and prove several abstract properties based on termination criteria. Then, we instantiate the high-level replacement systems by attributed graph transformation systems and present concrete termination criteria. We explore some types of rules and replacement units for which the criterion can be established. These are used to show the termination of some replacement units needed to express model transformations formalizing refactoring.

Termination of High-Level Replacement Units with Application to Model Transformation

Visual rewriting techniques, in particular graph transformations, are increasingly used to model transformations of systems specified through diagrammatic sentences. Several rewriting models have been proposed, differing in the expressivity of the types of rules and in the complexity of the rewriting mechanism; yet basic results concerning the formal properties of these models are still missing for many of them. In this paper, we propose a contribution towards solving the termination problem for rewriting systems with external control mechanisms. In particular, we obtain results of more general validity by extending the concept of transformation unit to high-level replacement systems, a generalization of graph transformation systems. For high-level replacement units, we state and prove several abstract properties based on termination criteria. Then, we instantiate the high-level replacement systems by attributed graph transformation systems and present concrete termination criteria. These are used to show the termination of some replacement units needed to express model transformations as a consequence of software refactoring.