Attributed Graph Transformation 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.

Parallel rewriting of attributed graphs

Some computations can be elegantly presented as the parallel or simultaneous application of rules. This is the case of cellular automata and of simultaneous assignments in Python. In both cases the expected result cannot be obtained by a sequential application of rules. A general framework of attributed graph transformations is proposed where such computations can be expressed and analyzed. Determinism is achieved by an exhaustive parallel application of rules, as in cellular automata that are shown to have a straightforward representation in this framework. A more concise parallel transformation is also proposed, where some applications of rules can be ignored thanks to their symmetries, while preserving determinism. Parallel transformations are then used to characterize the property of parallel independence.

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.

Applications of typed lambda-terms to categorical attributed graph transformations

This paper deals with modal transformation based on attributed graph rewriting. Our contribution investigates f single pushout approach for applying the rewrite rules. The computation of graph attributes is obtained through the use of lambda-terms in a typed lambda calculus with inductive types. In this paper we present solutions to cope with single pushout construction for the graph structure and the computations functions. As the rewrite systen use inductiv types, the expressive power of attribute computations increases and appears to be more efficient than the one based on sigma-algebras. Some examples showing the interest of our computation approach are described in this paper.

Attributed graph transformation with inheritance: Efficient conflict detection and local confluence analysis using abstract critical pairs

Inheritance is an important and widely spread concept enabling the elegant expression of hierarchy in object-oriented software programs or models. It has been defined for graphs and graph transformations enhancing the applicability of this formal technique. Up to now, for the analysis of transformations with inheritance a flattening construction has been used, which yields all the well-known results for graph transformation but results in a large number of graphs and rules that have to be analyzed.In this paper, we introduce a new category of typed attributed graphs with inheritance. For the detection of conflicts between graph transformations on these graphs, the notion of abstract critical pairs is defined. This allows us to perform the analysis on polymorphic rules and transformations without the need for flattening, which significantly increases the efficiency of the analysis and eases the interpretation of the analysis results. The new main result is the Local Confluence Theorem for typed attributed graph transformation with inheritance using abstract critical pairs. All constructions and results are demonstrated on an example for the analysis of refactorings.

Lazy Graph Transformation

Applying an attributed graph transformation rule to a given object graph always implies some kind of constraint solving. In many cases, the given constraints are almost trivial to solve. For instance, this is the case when a rule describes a transformation G ⇒ H, where the attributes of H are obtained by some simple computation from the attributes of G. However there are many other cases where the constraints to solve may be not so trivial and, moreover, may have several answers. This is the case, for instance, when the transformation process includes some kind of searching. In the current approaches to attributed graph transformation these constraints must be completely solved when defining the matching of the given transformation rule. This kind of early binding is well-known from other areas of Computer Science to be inadequate. For instance, the solution chosen for the constraints associated to a given transformation step may be not fully adequate, meaning that later, in the search for a better solution, we may need to backtrack this transformation step. In this paper, based on our previous work on the use of symbolic graphs to deal with different aspects related with attributed graphs, including attributed graph transformation, we present a new approach that, based on the new notion of narrowing graph transformation rule, allows us to delay constraint solving when doing attributed graph transformation, in a way that resembles lazy computation. For this reason, we have called lazy this new kind of transformation. Moreover, we show that the approach is sound and complete with respect to standard attributed graph transformation. A running example, where a graph transformation system describes some basic operations of a travel agency, shows the practical interest of the approach.

Formal Specification of Model Transformations by Triple Graph Grammars with Application Conditions

Triple graph grammars are a successful approach to describe exogenous model transformations, i.e. transformations between models conforming to differ- ent meta-models. Source and target models are related by some connection part, triple rules describe the simultaneous construction of these parts, and forward and backward rules can be derived modeling the forward and backward model transfor- mations. As shown already for the specification of visual models by typed attributed graph transformation, the expressiveness of the approach can be enhanced signifi- cantly by using application conditions, which are known to be equivalent to first order logic on graphs. In this paper, we extend triple rules with a specific form of application conditions, which enhance the expressiveness of formal specifications for model transforma- tions. We show how to extend results concerning information preservation, termi- nation, correctness, and completeness of model transformations to the case with application conditions. We illustrate our approach and results with a model trans- formation from statecharts to Petri nets.

Typed lambda-terms in categorical attributed graph transformation

This paper deals with model transformation based on attributed graph rewriting. Our contribution investigates a single pushout approach for applying the rewrite rules. The computation of graph attributes is obtained through the use of typed lambda-calculus with inductive types. In this paper we present solutions to cope with single pushout construction for the graph structure and the computations functions. As this rewrite system uses inductive types, the expressiveness of attribute computations is facilitated and appears more efficient than the one based on Sigma-algebras. Some examples showing the interest of our computation approach are described in this paper.

A Typed Attributed Graph Grammar with Inheritance for the Abstract Syntax of UML Class and Sequence Diagrams

According to the UML Standard 2.0 class and sequence diagrams are defined in a descriptive way by a MOF meta-model and semi-formal constraints. This paper presents a formal and constructive definition of the abstract syntax of UML class and sequence diagrams based on the well-defined theory of typed attributed graph transformation with inheritance and application conditions. The generated language covers all important features of these parts of UML diagrams and is shown to satisfy all of the corresponding constraints by construction. An explicit model transformation demonstrates the close correspondence between the graph grammar and the MOF definition of UML class and sequence diagrams. The graph grammar is validated by well-established benchmarks showing that all important features of the MOF definition of UML are covered. This formal constructive syntax definition of UML class and sequence diagrams is the basis for syntax directed editing, formal analysis, formal operational and denotational semantics and correctness of model transformations.

Attributed graph transformation with node type inheritance

The aim of this paper is to integrate typed attributed graph transformation with node type inheritance. Borrowing concepts from object oriented systems, the main idea is to enrich the attributed type graph with an inheritance relation and a set of abstract nodes. In this way, a node type inherits the attributes and edges of all its ancestors. Based on these concepts, it is possible to define abstract productions, containing abstract nodes. These productions are equivalent to a number of concrete productions, resulting from the substitution of the abstract node types by the node types in their inheritance clan. Therefore, productions become more compact and suitable for their use in combination with meta-modelling. The main results of this paper show that attributed graph transformation with node type inheritance is fully compatible with the existing concept of typed attributed graph transformation.

Towards Model Transformation in Generated Eclipse Editor Plug-Ins

With the growing importance of model-driven development, the ability of transforming models into well-defined semantic domains becomes a key to automated code generation or verification in the software development process. In this paper, we describe a high-level concept for specifying model transformations by means of typed, attributed graph transformation at the level of formal visual language specifications for the source and the target language. At the implementation level, a graph-transformation based generator of visual editor Eclipse plug-ins from formal visual language specifications has been developed. On the basis of this generator we discuss concepts for an implementation of the presented model transformation concepts and for an integration with the generated Eclipse plug-ins. We explain the concepts for model transformation and their implementation along a concrete model transformation from activity diagrams to Petri nets.

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.

A Conceptual and Formal Framework for the Integration of Data Type and Process Modeling Techniques

A conceptual framework for the integration of data type and process modeling techniques, called integration paradigm, has been presented by the authors in previous papers already. The aim of this paper is to give a short review of this conceptual framework and to present a formal model for the integration paradigm. The formal model for the four layers, called data type, data states and transformations, processes and system architecture layers respectively, is based on an integration of abstract data types and structured transition systems. This formal model can be instantiated by all kinds of basic and integrated modeling techniques. Algebraic high-level nets, attributed graph transformation, an integration of Z with statecharts, and some diagram techniques of UML are discussed on the conceptual level. As instantiation of the formal model, a well-known CCS sender specification, place/transition nets, algebraic high-level nets and attributed graph transformation are presented in this paper, while instantiations of other modeling techniques will be discussed elsewhere.