An Algebra of Hierarchical Graphs

We define an algebraic theory of hierarchical graphs, whose axioms characterise graph isomorphism: two terms are equated exactly when they represent the same graph. Our algebra can be understood as a high-level language for describing graphs with a node-sharing, embedding structure, and it is then well suited for defining graphical representations of software models where nesting and linking are key aspects

Conditional Bigraphs

Bigraphs are a universal graph based model, designed for analysing reactive systems that include spatial and non-spatial (e.g. communication) relationships. Bigraphs evolve over time using a rewriting framework that finds instances of a (sub)-bigraph, and substitutes a new bigraph. In standard bigraphs, the applicability of a rewrite rule is determined completely by a local match and does not allow any non-local reasoning, i.e. contextual conditions. We introduce conditional bigraphs that add conditions to rules and show how these fit into the matching framework for standard bigraphs. An implementation is provided, along with a set of examples. Finally, we discuss the limits of application conditions within the existing matching framework and present ways to extend the range of conditions that may be expressed

Translating model simulators to analysis models

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-540-78743-3_6Proceedings of 11th International Conference, FASE 2008, Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2008, Budapest, Hungary, March 29-April 6, 2008.We present a novel approach for the automatic generation of model-to-model transformations given a description of the operational semantics of the source language by means of graph transformation rules. The approach is geared to the generation of transformations from Domain-Specific Visual Languages (DSVLs) into semantic domains with an explicit notion of transition, like for example Petri nets. The generated transformation is expressed in the form of operational triple graph grammar rules that transform the static information (initial model) and the dynamics (source rules and their execution control structure). We illustrate these techniques with a DSVL in the domain of production systems, for which we generate a transformation into Petri nets.Work sponsored by the Spanish Ministry of Science and Education, project MOSAIC (TSI2005-08225-C07-06

Rewriting modulo symmetric monoidal structure

String diagrams are a powerful and intuitive graphical syntax for terms of symmetric monoidal categories (SMCs). They find many applications in computer science and are becoming increasingly relevant in other fields such as physics and control theory.An important role in many such approaches is played by equational theories of diagrams, typically oriented and applied as rewrite rules. This paper lays a comprehensive foundation for this form of rewriting. We interpret diagrams combinatorially as typed hypergraphs and establish the precise correspondence between diagram rewriting modulo the laws of SMCs on the one hand and double pushout (DPO) rewriting of hypergraphs, subject to a soundness condition called convexity, on the other. This result rests on a more general characterisation theorem in which we show that typed hypergraph DPO rewriting amounts to diagram rewriting modulo the laws of SMCs with a chosen special Frobenius structure.We illustrate our approach with a proof of termination for the theory of non-commutative bimonoids

Graphical Reasoning in Compact Closed Categories for Quantum Computation

Compact closed categories provide a foundational formalism for a variety of important domains, including quantum computation. These categories have a natural visualisation as a form of graphs. We present a formalism for equational reasoning about such graphs and develop this into a generic proof system with a fixed logical kernel for equational reasoning about compact closed categories. Automating this reasoning process is motivated by the slow and error prone nature of manual graph manipulation. A salient feature of our system is that it provides a formal and declarative account of derived results that can include `ellipses'-style notation. We illustrate the framework by instantiating it for a graphical language of quantum computation and show how this can be used to perform symbolic computation.Comment: 21 pages, 9 figures. This is the journal version of the paper published at AIS

Exploiting the Hierarchical Structure of Rule-Based Specifications for Decision Planning

Rule-based specifications have been very successful as a declarative approach in many domains, due to the handy yet solid foundations offered by rule-based machineries like term and graph rewriting. Realistic problems, however, call for suitable techniques to guarantee scalability. For instance, many domains exhibit a hierarchical structure that can be exploited conveniently. This is particularly evident for composition associations of models. We propose an explicit representation of such structured models and a methodology that exploits it for the description and analysis of model- and rule-based systems. The approach is presented in the framework of rewriting logic and its efficient implementation in the rewrite engine Maude and is illustrated with a case study.

Inter-modelling: From Theory to Practice

Proocedings of: ACM/IEEE 13 th International Conference on Model Driven Engineering Languages and Systems. Oslo, Norway, October 3-8, 2010.We define inter-modelling as the activity of building models that describe how modelling languages should be related. This includes many common activities in Model Driven Engineering, like the specification of model-to-model transformations, the definition of model matching and model traceability constraints, the development of inter-model consistency maintainers and exogenous model management operators. Recently, we proposed a formal approach to specify the allowed and forbidden relations between two modelling languages by means of bidirectional declarative patterns. Such specifications were used to generate graph rewriting rules able to enforce the relations in (forward and backward) model-to-model transformation scenarios. In this paper we extend the usage of patterns for two further inter-modelling scenarios &- model matching and model traceability &- and report on an EMF-based tool implementing them. The tool allows a high-level analysis of specifications based on the theory developed so far, as well as manipulation of traces by compilation of patterns into the Epsilon Object Language.Work funded by the Spanish Ministry of Science (project TIN2008-02081 and grants JC2009-00015, PR2009-0019), the R&D programme of the Madrid Region (project S2009/TIC-1650), the European Commission’s 7th Framework programme (grant #248864 (MADES)), and the Engineering and Physical Sciences Research Council (EPSRC) (grant EP/E034853/1).Publicad