What Algebraic Graph Transformations Can Do For Model Transformations

Model transformations are key activities in model-driven development (MDD). A number of model transformation approaches have emerged for different purposes and with different backgrounds. This paper focusses on the use of algebraic graph transformation concepts to specify and verify model transformations in MDD

Transformation of Attributed Structures with Cloning (Long Version)

Copying, or cloning, is a basic operation used in the specification of many applications in computer science. However, when dealing with complex structures, like graphs, cloning is not a straightforward operation since a copy of a single vertex may involve (implicitly)copying many edges. Therefore, most graph transformation approaches forbid the possibility of cloning. We tackle this problem by providing a framework for graph transformations with cloning. We use attributed graphs and allow rules to change attributes. These two features (cloning/changing attributes) together give rise to a powerful formal specification approach. In order to handle different kinds of graphs and attributes, we first define the notion of attributed structures in an abstract way. Then we generalise the sesqui-pushout approach of graph transformation in the proposed general framework and give appropriate conditions under which attributed structures can be transformed. Finally, we instantiate our general framework with different examples, showing that many structures can be handled and that the proposed framework allows one to specify complex operations in a natural way

Normal Factor Graphs and Holographic Transformations

This paper stands at the intersection of two distinct lines of research. One line is "holographic algorithms," a powerful approach introduced by Valiant for solving various counting problems in computer science; the other is "normal factor graphs," an elegant framework proposed by Forney for representing codes defined on graphs. We introduce the notion of holographic transformations for normal factor graphs, and establish a very general theorem, called the generalized Holant theorem, which relates a normal factor graph to its holographic transformation. We show that the generalized Holant theorem on the one hand underlies the principle of holographic algorithms, and on the other hand reduces to a general duality theorem for normal factor graphs, a special case of which was first proved by Forney. In the course of our development, we formalize a new semantics for normal factor graphs, which highlights various linear algebraic properties that potentially enable the use of normal factor graphs as a linear algebraic tool.Comment: To appear IEEE Trans. Inform. Theor

Simulating Multigraph Transformations Using Simple Graphs

Application of graph transformations for software verification and model transformation is an emergent field of research. In particular, graph transformation approaches provide a natural way of modelling object oriented systems and semantics of object-oriented languages.\ud \ud There exist a number of tools for graph transformations that are often specialised in a particular kind of graphs and/or graph transformation approaches, depending on the desired application domain. The main drawback of this diversity is the lack of interoperability.\ud \ud In this paper we show how (typed) multigraph production systems can be translated into (typed) simple-graph production systems. The presented construction enables the use of multigraphs with DPO transformation approach in tools that only support simple graphs with SPO transformation approach, e.g. the GROOVE tool

Evaluating the performance of model transformation styles in Maude

Rule-based programming has been shown to be very successful in many application areas. Two prominent examples are the specification of model transformations in model driven development approaches and the definition of structured operational semantics of formal languages. General rewriting frameworks such as Maude are flexible enough to allow the programmer to adopt and mix various rule styles. The choice between styles can be biased by the programmer’s background. For instance, experts in visual formalisms might prefer graph-rewriting styles, while experts in semantics might prefer structurally inductive rules. This paper evaluates the performance of different rule styles on a significant benchmark taken from the literature on model transformation. Depending on the actual transformation being carried out, our results show that different rule styles can offer drastically different performances. We point out the situations from which each rule style benefits to offer a valuable set of hints for choosing one style over the other

Singularity, complexity, and quasi--integrability of rational mappings

We investigate global properties of the mappings entering the description of symmetries of integrable spin and vertex models, by exploiting their nature of birational transformations of projective spaces. We give an algorithmic analysis of the structure of invariants of such mappings. We discuss some characteristic conditions for their (quasi)--integrability, and in particular its links with their singularities (in the 2--plane). Finally, we describe some of their properties {\it qua\/} dynamical systems, making contact with Arnol'd's notion of complexity, and exemplify remarkable behaviours.Comment: Latex file. 17 pages. To appear in CM

Category Theory and Model-Driven Engineering: From Formal Semantics to Design Patterns and Beyond

There is a hidden intrigue in the title. CT is one of the most abstract mathematical disciplines, sometimes nicknamed "abstract nonsense". MDE is a recent trend in software development, industrially supported by standards, tools, and the status of a new "silver bullet". Surprisingly, categorical patterns turn out to be directly applicable to mathematical modeling of structures appearing in everyday MDE practice. Model merging, transformation, synchronization, and other important model management scenarios can be seen as executions of categorical specifications. Moreover, the paper aims to elucidate a claim that relationships between CT and MDE are more complex and richer than is normally assumed for "applied mathematics". CT provides a toolbox of design patterns and structural principles of real practical value for MDE. We will present examples of how an elementary categorical arrangement of a model management scenario reveals deficiencies in the architecture of modern tools automating the scenario.Comment: In Proceedings ACCAT 2012, arXiv:1208.430