Ulrike Prange

Fundamental Theory for Typed Attributed Graph Transformation

The concept of typed attributed graph transformation is most significant for modeling and meta modeling in software engineering and visual languages, but up to now there is no adequate theory for this important branch of graph transformation. In this paper we give a new formalization of typed attributed graphs, which allows node and edge attribution. The first main result shows that the corresponding category is isomorphic to the category of algebras over a specific kind of attributed graph structure signature. This allows to prove the second main result showing that the category of typed attributed graphs is an instance of “adhesive HLR categories”. This new concept combines adhesive categories introduced by Lack and Sobocinski with the well-known approach of high-level replacement (HLR) systems using a new simplified version of HLR conditions. As a consequence we obtain a rigorous approach to typed attributed graph transformation providing as fundamental results the Local Church-Rosser, Parallelism, Concurrency, Embedding and Extension Theorem and a Local Confluence Theorem known as Critical Pair Lemma in the literature.

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.

Adhesive High-Level Replacement Categories and Systems

Adhesive high-level replacement (HLR) categories and systems are introduced as a new categorical framework for graph transformation in a broad sense, which combines the well-known concept of HLR systems with the new concept of adhesive categories introduced by Lack and Sobocinski.

Termination analysis of model transformations by petri nets

Despite the increasing relevance of model transformation techniques in model-driven software development, research is mainly conducted to the specification and the automation of such transformations. However, since the transformations themselves may also contain conceptual flaws, it is essential to formally analyze them prior to executing them on user models. In the current paper, we focus on a central validation problem of trusted model transformations, namely, termination and propose a Petri net based analysis method that provides a sufficient criterion for the termination problem of model transformations captured by graph transformation systems.

On-the-Fly Construction, Correctness and Completeness of Model Transformations Based on Triple Graph Grammars

Triple graph grammars (TGGs) are a formal and intuitive concept for the specification of model transformations. Their main advantage is an automatic derivation of operational rules for bidirectional model transformations, which simplifies specification and enhances usability as well as consistency. In this paper we continue previous work on the formal definition of model transformations based on triple graph rules with negative application conditions (NACs). The new notion of partial source consistency enables us to construct consistent model transformations on-the-fly instead of analyzing consistency of completed model transformations. We show the crucial properties termination, correctness and completeness (including NAC-consistency) for the model transformations resulting from our construction. Moreover, we define parallel independence for model transformation steps which allows us to perform partial-order reduction in order to improve efficiency. The results are applicable to several relevant model transformations and in particular to our example transformation from class diagrams to database models.

A logic of graph constraints

Graph constraints were introduced in the area of graph transformation, in connection with the notion of (negative) application conditions, as a form to limit the applicability of transformation rules. However, we believe that graph constraints may also play a significant role in the area of visual software modelling or in the specification and verification of semi-structured documents or websites (i.e. HTML or XML sets of documents). In this sense, after some discussion on these application areas, we concentrate on the problem of how to prove the consistency of specifications based on this kind of constraints. In particular, we present proof rules for three classes of (increasingly more powerful) graph constraints and show that our proof rules are sound and (refutationally) complete for each class.

Petri Net Transformations

Abstract Petri Nets: A Uniform Approach and Rule-Based Refinement. PhD thesis, Technical University Berlin, 1996. Shaker Verlag. [23] J. Padberg. Categorical Approach to Horizontal Structuring and Refinement of High-Level Replacement Systems. Applied Categorical Structures, 7(4):371-403, 1999. [24] J. Padberg. Basic Ideas for Transformations of Specification Architectures. In Proc.Workshop on Software Evolution through Transformations (SET 02), volume 74 of ENTCS, 2002. [25] J. Padberg, H. Ehrig, and L. Ribeiro. Algebraic High-Level Net Transformation Systems. Mathematical Structures in Computer Science, 5(2):217-256, 1995. [26] J. Padberg, P. Schiller, and H. Ehrig. New Concepts for High-Level Petri Nets in the Application Domain of Train Control. In Proc. Symposium on Transportation Systems, pages 153-160, 2000. [27] J. Padberg and M. Urbasek. Rule-Based Refinement of Petri Nets: A Survey. In Proc. Petri Net Technology for Communication-Based Systems, volume 2472 of LNCS, pages 161-196. Springer, 2003. [28] W. Reisig. Petri Nets and Algebraic Specifications.

Parallelism and Concurrency in Adhesive High-Level Replacement Systems with Negative Application Conditions

The goal of this paper is the generalization of parallelism and concurrency results for adhesive High-Level Replacement (HLR) systems to adhesive HLR systems with negative application conditions. These conditions restrict the application of a rule by expressing that a specific structure should not be present before or after applying the rule to a certain context. Such a condition influences thus each rule application or transformation and therefore changes significantly the properties of the replacement system. The effect of negative application conditions on parallelism and concurrency in the replacement system is described in the generalization of the following results, formulated already for adhesive HLR systems without negative application conditions: Local Church-Rosser Theorem, Parallelism Theorem and Concurrency Theorem. These important generalized results will support the development of formal analysis techniques for adhesive HLR systems with negative application conditions.

Introduction to AGG and EMF Tiger by modeling a Conference Scheduling System

In this paper, we focus on the Conference Scheduling System, a case study at the Tool Contest of Graph-Based Tools (GraBaTs) 2008. We took part in the contest with our graph transformation tool AGG and the Eclipse-based EMF model transformation tool EMF Tiger. We present the features of both tools and evaluate their abilities to model the Conference Scheduling System and to deal with additional contest assignments like model instance generation, property verification, and interoperability.

Transformations in Reconfigurable Place/Transition Systems

Reconfigurable place/transition systems are Petri nets with initial markings and a set of rules which allow the modification of the net during runtime in order to adapt the net to new requirements. For the transformation of Petri nets in the double pushout approach, the categorical framework of adhesive high-level replacement systems has been instantiated to Petri nets. In this paper, we show that also place/transition systems form a weak adhesive high-level replacement category. This allows us to apply the developed theory also to tranformations within reconfigurable place/transition systems.