Correctness, completeness and termination of pattern-based model-to-model transformation

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-642-03741-2_26Proceedings of Third International Conference, CALCO 2009, Udine, Italy, September 7-10, 2009.Model-to-model (M2M) transformation consists in trans- forming models from a source to a target language. Many transformation languages exist, but few of them combine a declarative and relational style with a formal underpinning able to show properties of the transformation. Pattern-based transformation is an algebraic, bidirectional, and relational approach to M2M transformation. Specifications are made of patterns stating the allowed or forbidden relations between source and target models, and then compiled into low level operational mechanisms to perform source-to-target or target-to-source transformations. In this paper, we study the compilation into operational triple graph grammar rules and show: (i) correctness of the compilation of a specification without negative patterns; (ii) termination of the rules, and (iii) completeness, in the sense that every model considered relevant can be built by the rules.Work supported by the Spanish Ministry of Science and Innovation, projects METEORIC (TIN2008-02081), MODUWEB (TIN2006-09678) and FORMALISM (TIN2007-66523). Moreover, part of this work was done during a sabbatical leave of the first author at TU Berlin, with financial support from the Spanish Ministry of Science and Innovation (grant ref. PR2008-0185). We thank the referees for their useful comment

Characterizing Van Kampen Squares via Descent Data

Categories in which cocones satisfy certain exactness conditions w.r.t. pullbacks are subject to current research activities in theoretical computer science. Usually, exactness is expressed in terms of properties of the pullback functor associated with the cocone. Even in the case of non-exactness, researchers in model semantics and rewriting theory inquire an elementary characterization of the image of this functor. In this paper we will investigate this question in the special case where the cocone is a cospan, i.e. part of a Van Kampen square. The use of Descent Data as the dominant categorical tool yields two main results: A simple condition which characterizes the reachable part of the above mentioned functor in terms of liftings of involved equivalence relations and (as a consequence) a necessary and sufficient condition for a pushout to be a Van Kampen square formulated in a purely algebraic manner.Comment: In Proceedings ACCAT 2012, arXiv:1208.430

Borrowed contexts for attributed graphs

Borrowed context graph transformation is a simple and powerful technique developed by Ehrig and König that allow us to derive labeled transitions and bisimulation congruences for graph transformation systems or, in general, for pocess calculi that can be defined in terms of graph transformation systems. Moreover, the same authors have also shown how to use this technique for the verification of bisimilarity. In principle, the main results about borrowed context transformation do not apply only to plain graphs, but they are generic in the sense that they apply to all categories tha satisfy certain properties related to the notion of adhesivity. In particular, this is the case of attributed graphs. However, as we show in the paper, the techniques used for checking bisimilarity are not equally generic and, in particular they fail, if we want to apply them to attributed graphs. To solve this problem, in this paper, we define a special notion of symbolic graph bisimulation and show how it can be used to check bisimilarity of attributed graphs.Postprint (published version

Synthesis of OCL Pre-conditions for Graph Transformation Rules

Proceedings of: Third International Conference on Model Transformation (ICMT 2010): Theory and Practice of Model Transformation. Málaga, Spain, 28 June-02 July, 2010Graph transformation (GT) is being increasingly used in Model Driven Engineering (MDE) to describe in-place transformations like animations and refactorings. For its practical use, rules are often complemented with OCL application conditions. The advancement of rule post-conditions into pre-conditions is a well-known problem in GT, but current techniques do not consider OCL. In this paper we provide an approach to advance post-conditions with arbitrary OCL expressions into pre-conditions. This presents benefits for the practical use of GT in MDE, as it allows: (i) to automatically derive pre-conditions from the meta-model integrity constraints, ensuring rule correctness, (ii) to derive pre-conditions from graph constraints with OCL expressions and (iii) to check applicability of rule sequences with OCL conditions.Work funded by the Spanish Ministry of Science and Innovation through projects “Design and construction of a Conceptual Modeling Assistant” (TIN2008-00444/TIN - Grupo Consolidado), “METEORIC” (TIN2008-02081),mobility grants JC2009-00015 and PR2009-0019, and the R&D program of the Community of Madrid (S2009/TIC-1650, project “e-Madrid”).Publicad

Representing First-Order Logic Using Graphs

Abstract. We show how edge-labelled graphs can be used to represent first-order logic formulae. This gives rise to recursively nested structures, in which each level of nesting corresponds to the negation of a set of existentials. The model is a direct generalisation of the negative application conditions used in graph rewriting, which count a single level of nesting and are thereby shown to correspond to the fragment ∃¬∃ of first-order logic. Vice versa, this generalisation may be used to strengthen the notion of application conditions. We then proceed to show how these nested models may be flattened to (sets of) plain graphs, by allowing some structure on the labels. The resulting formulae-as-graphs may form the basis of a unification of the theories of graph transformation and predicate transformation

Pattern-based model-to-model transformation: Handling attribute conditions

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-642-02408-5_7Proceedings of Second International Conference, ICMT 2009, Zurich, Switzerland, June 29-30, 2009Pattern-based model-to-model transformation is a new approach for specifying transformations in a declarative, relational and formal style. The language relies on patterns describing allowed or forbidden relations between two models, which are compiled into operational mechanisms to perform forward and backward transformations. In this paper, we extend the approach for handling attribute conditions expressed in some suitable logic, adapt the operational mechanisms based on graph transformation to relax attribute handling by constraint solving, and discuss heuristics for the compilation of patterns into rules.Work supported by the Spanish Ministry of Science and Innovation, projects METEORIC (TIN2008-02081),MODUWEB (TIN2006-09678) and FORMALISM (TIN2007-66523).Moreover, part of this work was done during a sabbatical leave of the third author at TU Berlin, with financial support from the Ministerio de Ciencia e Innovaci´on (grant ref. PR2008-0185). We thank the referees for their useful comment

On insertion-deletion systems over relational words

We introduce a new notion of a relational word as a finite totally ordered set of positions endowed with three binary relations that describe which positions are labeled by equal data, by unequal data and those having an undefined relation between their labels. We define the operations of insertion and deletion on relational words generalizing corresponding operations on strings. We prove that the transitive and reflexive closure of these operations has a decidable membership problem for the case of short insertion-deletion rules (of size two/three and three/two). At the same time, we show that in the general case such systems can produce a coding of any recursively enumerable language leading to undecidabilty of reachability questions.Comment: 24 pages, 8 figure

Maximum-entropy theory of steady-state quantum transport

We develop a theoretical framework for describing steady-state quantum transport phenomena, based on the general maximum-entropy principle of nonequilibrium statistical mechanics. The general form of the many-body density matrix is derived, which contains the invariant part of the current operator that guarantees the nonequilibrium and steady-state character of the ensemble. Several examples of the theory are given, demonstrating the relationship of the present treatment to the widely used scattering-state occupation schemes at the level of the self-consistent single-particle approximation. The latter schemes are shown not to maximize the entropy, except in certain limits