An Abstract Module Concept for Graph Transformation Systems

Graph transformation systems are a well known formal specification technique that support the rule based specification of the dynamic behaviour of systems. Recently, many specification languages for graph transformation systems have been developed, and modularization techniques are then needed in order to deal with large and complex graph transformation specifications, to enhance the reuse of specifications, and to hide implementation details. In this paper we present an abstract categorical approach to modularization of graph transformation systems. Modules are called cat–modules and defined over a generic category cat of graph transformation specifications and morphisms. We describe the main characteristics and properties of cat–modules, their interconnection operations, namely union, composition and refinement of modules, and some compatibility properties between such operations

A formal support to business and architectural design for service-oriented systems

Architectural Design Rewriting (ADR) is an approach for the design of software architectures developed within Sensoria by reconciling graph transformation and process calculi techniques. The key feature that makes ADR a suitable and expressive framework is the algebraic handling of structured graphs, which improves the support for specification, analysis and verification of service-oriented architectures and applications. We show how ADR is used as a formal ground for high-level modelling languages and approaches developed within Sensoria

A visual workspace for constructing hybrid MDS algorithms and coordinating multiple views

Data can be distinguished according to volume, variable types and distribution, and each of these characteristics imposes constraints upon the choice of applicable algorithms for their visualisation. This has led to an abundance of often disparate algorithmic techniques. Previous work has shown that a hybrid algorithmic approach can be successful in addressing the impact of data volume on the feasibility of multidimensional scaling (MDS). This paper presents a system and framework in which a user can easily explore algorithms as well as their hybrid conjunctions and the data flowing through them. Visual programming and a novel algorithmic architecture let the user semi-automatically define data flows and the co-ordination of multiple views of algorithmic and visualisation components. We propose that our approach has two main benefits: significant improvements in run times of MDS algorithms can be achieved, and intermediate views of the data and the visualisation program structure can provide greater insight and control over the visualisation process

2-cosemisimplicial objects in a 2-category, permutohedra and deformations of pseudofunctors

In this paper we take up again the deformation theory for $K$-linear pseudofunctors initiated in a previous work (Adv. Math. 182 (2004) 204-277). We start by introducing a notion of a 2-cosemisimplicial object in an arbitrary 2-category and analyzing the corresponding coherence question, where the permutohedra make their appearence. We then describe a general method to obtain cochain complexes of K-modules from (enhanced) 2-cosemisimplicial objects in the 2-category ${\bf Cat}_K$ of small $K$-linear categories and prove that the deformation complex introduced in the above mentioned work can be obtained by this method from a 2-cosemisimplicial object that can be associated to the pseudofunctor. Finally, using a generalization to the context of $K$-linear categories of the deviation calculus introduced by Markl and Stasheff for $K$-modules (J. Algebra 170 (1994) 122), it is shown that the obstructions to the integrability of an $n^{th}$-order deformation of a pseudofunctor indeed correspond to cocycles in the third cohomology group, a question which remained open in our previous work.Comment: 43 pages, 6 figures; this is the revised version as published in the JPA

On the (non-)existence of polynomial kernels for Pl-free edge modification problems

Given a graph G = (V,E) and an integer k, an edge modification problem for a graph property P consists in deciding whether there exists a set of edges F of size at most k such that the graph H = (V,E \vartriangle F) satisfies the property P. In the P edge-completion problem, the set F of edges is constrained to be disjoint from E; in the P edge-deletion problem, F is a subset of E; no constraint is imposed on F in the P edge-edition problem. A number of optimization problems can be expressed in terms of graph modification problems which have been extensively studied in the context of parameterized complexity. When parameterized by the size k of the edge set F, it has been proved that if P is an hereditary property characterized by a finite set of forbidden induced subgraphs, then the three P edge-modification problems are FPT. It was then natural to ask whether these problems also admit a polynomial size kernel. Using recent lower bound techniques, Kratsch and Wahlstrom answered this question negatively. However, the problem remains open on many natural graph classes characterized by forbidden induced subgraphs. Kratsch and Wahlstrom asked whether the result holds when the forbidden subgraphs are paths or cycles and pointed out that the problem is already open in the case of P4-free graphs (i.e. cographs). This paper provides positive and negative results in that line of research. We prove that parameterized cograph edge modification problems have cubic vertex kernels whereas polynomial kernels are unlikely to exist for the Pl-free and Cl-free edge-deletion problems for large enough l