Using matrix graph grammars for the analysis of behavioural specifications: Sequential and parallel independence

Proceedings of the Seventh Spanish Conference on Programming and Computer Languages (PROLE 2007)In this paper we present a new approach for the analysis of rule-based specification of system dynamics. We model system states as simple digraphs, which can be represented with boolean matrices. Rules modelling the different state changes of the system can also be represented with boolean matrices, and therefore the rewriting is expressed using boolean operations only. The conditions for sequential independence between pair of rules are well-known in the categorical approaches to graph transformation (e.g. single and double pushout). These conditions state when two rules can be applied in any order yielding the same result. In this paper, we study the concept of sequential independence in our framework, and extend it in order to consider derivations of arbitrary finite length. Instead of studying one-step rule advances, we study independence of rule permutations in sequences of arbitrary finite length. We also analyse the conditions under which a sequence is applicable to a given host graph. We introduce rule composition and give some preliminary results regarding parallel independence. Moreover, we improve our framework making explicit the elements which, if present, disable the application of a rule or a sequence.Work sponsored by Spanish Ministry of Science and Education, project MOSAIC (TSI2005-08225-C07-06)

Extending Partial 1-Planar Drawings

Algorithmic extension problems of partial graph representations such as planar graph drawings or geometric intersection representations are of growing interest in topological graph theory and graph drawing. In such an extension problem, we are given a tuple (G,H,?) consisting of a graph G, a connected subgraph H of G and a drawing ? of H, and the task is to extend ? into a drawing of G while maintaining some desired property of the drawing, such as planarity. In this paper we study the problem of extending partial 1-planar drawings, which are drawings in the plane that allow each edge to have at most one crossing. In addition we consider the subclass of IC-planar drawings, which are 1-planar drawings with independent crossings. Recognizing 1-planar graphs as well as IC-planar graphs is NP-complete and the NP-completeness easily carries over to the extension problem. Therefore, our focus lies on establishing the tractability of such extension problems in a weaker sense than polynomial-time tractability. Here, we show that both problems are fixed-parameter tractable when parameterized by the number of edges missing from H, i.e., the edge deletion distance between H and G. The second part of the paper then turns to a more powerful parameterization which is based on measuring the vertex+edge deletion distance between the partial and complete drawing, i.e., the minimum number of vertices and edges that need to be deleted to obtain H from G

Formalizing graphical notations

The thesis describes research into graphical notations for software engineering, with a principal interest in ways of formalizing them. The research seeks to provide a theoretical basis that will help in designing both notations and the software tools that process them. The work starts from a survey of literature on notation, followed by a review of techniques for formal description and for computational handling of notations. The survey concentrates on collecting views of the benefits and the problems attending notation use in software development; the review covers picture description languages, grammars and tools such as generic editors and visual programming environments. The main problem of notation is found to be a lack of any coherent, rigorous description methods. The current approaches to this problem are analysed as lacking in consensus on syntax specification and also lacking a clear focus on a defined concept of notated expression. To address these deficiencies, the thesis embarks upon an exploration of serniotic, linguistic and logical theory; this culminates in a proposed formalization of serniosis in notations, using categorial model theory as a mathematical foundation. An argument about the structure of sign systems leads to an analysis of notation into a layered system of tractable theories, spanning the gap between expressive pictorial medium and subject domain. This notion of 'tectonic' theory aims to treat both diagrams and formulae together. The research gives details of how syntactic structure can be sketched in a mathematical sense, with examples applying to software development diagrams, offering a new solution to the problem of notation specification. Based on these methods, the thesis discusses directions for resolving the harder problems of supporting notation design, processing and computer-aided generic editing. A number of future research areas are thereby opened up. For practical trial of the ideas, the work proceeds to the development and partial implementation of a system to aid the design of notations and editors. Finally the thesis is evaluated as a contribution to theory in an area which has not attracted a standard approach

A Systematic Approach to Constructing Families of Incremental Topology Control Algorithms Using Graph Transformation

In the communication systems domain, constructing and maintaining network topologies via topology control (TC) algorithms is an important cross-cutting research area. Network topologies are usually modeled using attributed graphs whose nodes and edges represent the network nodes and their interconnecting links. A key requirement of TC algorithms is to fulfill certain consistency and optimization properties to ensure a high quality of service. Still, few attempts have been made to constructively integrate these properties into the development process of TC algorithms. Furthermore, even though many TC algorithms share substantial parts (such as structural patterns or tie-breaking strategies), few works constructively leverage these commonalities and differences of TC algorithms systematically. In previous work, we addressed the constructive integration of consistency properties into the development process. We outlined a constructive, model-driven methodology for designing individual TC algorithms. Valid and high-quality topologies are characterized using declarative graph constraints; TC algorithms are specified using programmed graph transformation. We applied a well-known static analysis technique to refine a given TC algorithm in a way that the resulting algorithm preserves the specified graph constraints. In this paper, we extend our constructive methodology by generalizing it to support the specification of families of TC algorithms. To show the feasibility of our approach, we reneging six existing TC algorithms and develop e-kTC, a novel energy-efficient variant of the TC algorithm kTC. Finally, we evaluate a subset of the specified TC algorithms using a new tool integration of the graph transformation tool eMoflon and the Simonstrator network simulation framework.Comment: Corresponds to the accepted manuscrip

Correct-by-Construction Development of Dynamic Topology Control Algorithms

Wireless devices are influencing our everyday lives today and will even more so in the future. A wireless sensor network (WSN) consists of dozens to hundreds of small, cheap, battery-powered, resource-constrained sensor devices (motes) that cooperate to serve a common purpose. These networks are applied in safety- and security-critical areas (e.g., e-health, intrusion detection). The topology of such a system is an attributed graph consisting of nodes representing the devices and edges representing the communication links between devices. Topology control (TC) improves the energy consumption behavior of a WSN by blocking costly links. This allows a mote to reduce its transmission power. A TC algorithm must fulfill important consistency properties (e.g., that the resulting topology is connected). The traditional development process for TC algorithms only considers consistency properties during the initial specification phase. The actual implementation is carried out manually, which is error prone and time consuming. Thus, it is difficult to verify that the implementation fulfills the required consistency properties. The problem becomes even more severe if the development process is iterative. Additionally, many TC algorithms are batch algorithms, which process the entire topology, irrespective of the extent of the topology modifications since the last execution. Therefore, dynamic TC is desirable, which reacts to change events of the topology. In this thesis, we propose a model-driven correct-by-construction methodology for developing dynamic TC algorithms. We model local consistency properties using graph constraints and global consistency properties using second-order logic. Graph transformation rules capture the different types of topology modifications. To specify the control flow of a TC algorithm, we employ the programmed graph transformation language story-driven modeling. We presume that local consistency properties jointly imply the global consistency properties. We ensure the fulfillment of the local consistency properties by synthesizing weakest preconditions for each rule. The synthesized preconditions prohibit the application of a rule if and only if the application would lead to a violation of a consistency property. Still, this restriction is infeasible for topology modifications that need to be executed in any case. Therefore, as a major contribution of this thesis, we propose the anticipation loop synthesis algorithm, which transforms the synthesized preconditions into routines that anticipate all violations of these preconditions. This algorithm also enables the correct-by-construction runtime reconfiguration of adaptive WSNs. We provide tooling for both common evaluation steps. Cobolt allows to evaluate the specified TC algorithms rapidly using the network simulator Simonstrator. cMoflon generates embedded C code for hardware testbeds that build on the sensor operating system Contiki

Technical Dimensions of Programming Systems

Programming requires much more than just writing code in a programming language. It is usually done in the context of a stateful environment, by interacting with a system through a graphical user interface. Yet, this wide space of possibilities lacks a common structure for navigation. Work on programming systems fails to form a coherent body of research, making it hard to improve on past work and advance the state of the art. In computer science, much has been said and done to allow comparison of programming languages, yet no similar theory exists for programming systems; we believe that programming systems deserve a theory too. We present a framework of technical dimensions which capture the underlying characteristics of programming systems and provide a means for conceptualizing and comparing them. We identify technical dimensions by examining past influential programming systems and reviewing their design principles, technical capabilities, and styles of user interaction. Technical dimensions capture characteristics that may be studied, compared and advanced independently. This makes it possible to talk about programming systems in a way that can be shared and constructively debated rather than relying solely on personal impressions. Our framework is derived using a qualitative analysis of past programming systems. We outline two concrete ways of using our framework. First, we show how it can analyze a recently developed novel programming system. Then, we use it to identify an interesting unexplored point in the design space of programming systems. Much research effort focuses on building programming systems that are easier to use, accessible to non-experts, moldable and/or powerful, but such efforts are disconnected. They are informal, guided by the personal vision of their authors and thus are only evaluable and comparable on the basis of individual experience using them. By providing foundations for more systematic research, we can help programming systems researchers to stand, at last, on the shoulders of giants

A cognitive exploration of the “non-visual” nature of geometric proofs

Why are Geometric Proofs (Usually) “Non-Visual”? We asked this question as a way to explore the similarities and differences between diagrams and text (visual thinking versus language thinking). Traditional text-based proofs are considered (by many to be) more rigorous than diagrams alone. In this paper we focus on human perceptual-cognitive characteristics that may encourage textual modes for proofs because of the ergonomic affordances of text relative to diagrams. We suggest that visual-spatial perception of physical objects, where an object is perceived with greater acuity through foveal vision rather than peripheral vision, is similar to attention navigating a conceptual visual-spatial structure. We suggest that attention has foveal-like and peripheral-like characteristics and that textual modes appeal to what we refer to here as foveal-focal attention, an extension of prior work in focused attention

Automatisches Zeichnen von Graphen für modellgetriebene Softwareentwicklung

As shown previously by Fuhrmann, there are several concepts for increasing the productivity of MDE by improving the practical handling of models. The automatic layout of graph-based models is a key enabler in this context. However, there is a striking contrast between the abundance of research results in the field of graph layout methods and the current state of graphical modeling tools, where only a tiny fraction of these results are ever adopted. This thesis aims to bridge this gap on three separate levels: specialized layout algorithms, configuration management, and software infrastructure. Regarding layout algorithms, here we focus on the layer-based approach. We examine its extension to include ports and hyperedges, which are essential features of certain kinds of graphs, e.g. data flow models. The main contribution is the handling of constraints on the positioning of ports, which is done mainly in the crossing minimization and edge routing phases. Hyperedges are represented with normal edges, simplifying their handling but introducing inaccuracies for counting crossings. A final extension discussed here is a sketch-driven approach for simple integration of user interactivity. An abstract layout is the selection of a layout algorithm with a mapping of its parameters to specific values. We discuss a new meta model allowing to specify the structure of a graph as well as its abstract layout and its concrete layout, i.e. positioning data computed by the layout algorithm. This forms a basis for efficient management of layout configurations. Furthermore, we investigate an evolutionary algorithm for searching the solution space of abstract layouts, taking readability criteria into account for evaluating solutions. The software infrastructure developed here targets the connection of arbitrary diagram viewers (front-ends) with arbitrary graph layout algorithms (back-ends). The main challenge is to find suitable abstractions that allow such generality and at the same time keep the complexity as low as possible. We discuss a possible realization based on the Eclipse platform, which is used by several modeling tools, e.g. the Graphical Modeling Framework. A web-based survey has been conducted among users of the layout infrastructure in order to evaluate to what extent the stated goals have been met. The overall feedback collected from this survey is very positive.Wie bereits von Fuhrmann gezeigt, kann die Produktivität modellgetriebener Softwareentwicklung durch zahlreiche Konzepte zur Verbesserung der praktischen Handhabung von Modellen erhöht werden. Dabei ist das automatische Layout graphenbasierter Modelle ein zentraler Schlüssel. Allerdings gibt es einen bemerkenswerten Kontrast zwischen der Fülle an Forschungsergebnissen im Bereich des Graphen-Layout und dem aktuellen Stand graphischer Modellierungswerkzeuge, bei denen nur ein kleiner Teil dieser Ergebnisse übernommen wird. Das Ziel dieser Arbeit ist diese Lücke auf drei separaten Ebenen zu überbrücken: spezialisierte Layout-Algorithmen, Verwaltung von Konfigurationen und Software-Infrastruktur. Im Bezug auf Layout-Algorithmen liegt der Schwerpunkt auf dem Layer-basierten Ansatz. Wir untersuchen dessen Erweiterung zur Unterstützung von Ports und Hyperkanten, was wesentliche Bestandteile bestimmter Arten von Graphen sind, z.B. Datenflussmodelle. Der Hauptbeitrag ist die Einbeziehung von Bedingungen für die Positionierung von Ports, vor allem während der Kreuzungsminimierung und der Kantenführungsphase. Hyperkanten werden durch normale Kanten repräsentiert, was deren Verarbeitung vereinfacht aber Ungenauigkeiten beim Zählen von Kreuzungen verursacht. Als letzte Erweiterung betrachten wir einen Sketch-basierten Ansatz für die einfache Integration von Nutzerinteraktivität. Ein abstraktes Layout ist die Auswahl eines Layout-Algorithmus zusammen mit einer Abbildung seiner Parameter auf konkrete Werte, während ein konkretes Layout Positionsdaten beschreibt, die von einem Algorithmus berechnet wurden. Wir diskutieren ein neues Metamodell, mit dem sowohl die Struktur als auch das abstrakte sowie das konkrete Layout eines Graphen spezifiziert werden kann. Dies bildet eine Grundlage für die effiziente Verwaltung von Layout-Konfigurationen. Zudem untersuchen wir einen evolutionären Algorithmus für die Suche im Lösungsraum abstrakter Layouts, wobei zur Bewertung von Lösungen Ästhetikkriterien ausgewertet werden. Die in dieser Arbeit entwickelte Software-Infrastruktur hat als Ziel, beliebige Graphen-basierte Diagramme (front-ends) mit beliebigen Layout-Algorithmen (back-ends) zu verbinden. Die größte Herausforderung dabei ist das Finden geeigneter Abstraktionen, die eine solche Allgemeingültigkeit erlauben und gleichzeitig die Komplexität so niedrig wie möglich halten. Wir betrachten eine mögliche Realisierung, die auf Eclipse basiert, eine von vielen Modellierungswerkzeugen verwendete Plattform. Eine Web-basierte Umfrage wurde unter Nutzern der Layout-Infrastruktur durchgeführt, um zu untersuchen inwieweit die gesteckten Ziele erfüllt worden sind. Die allgemeine Resonanz zu dieser Umfrage ist sehr positiv