The proceedings of the fourth Vienna Development Method Symposium, VDM'91, are published here in two volumes. Previous VDM symposia were held in 1987 (LNCS 252), 1988 (LNCS 328), and 1990 (LNCS 428). The VDM symposia have been organized by VDM Europe, formed in 1985 as an advisory board sponsored by the Commission of the European Communities. The VDM Europe working group consisted of researchers, software engineers, and programmers, allinterested in promoting the industrial usage of formal methods for software development. The fourth VDM symposium presented not only VDM but also a large number of other methods for formal software development. Volume 1 contains conference contributions. It has four parts: contributions of invited speakers, papers, project reports, and tools demonstration abstracts. The emphasis is on methods and calculi for development, verification and verification tools support, experiences from doing developments, and the associated theoretical problems. Volume 2 contains four introductory tutorials (on LARCH, Refinement Calculus, VDM, and RAISE) and four advanced tutorials (on ABEL, PROSPECTRA, The B Method, and The Stack). They present a comprehensive account of the state of theart.

This Festschrift volume, published in honor of Willem-Paul de Roever, contains 19 detailed papers written by the friends and colleagues of the honoree, all eminent scientists in their own right. These are preceded by a detailed bibliography and rounded off, at the end of the book, with a gallery of photographs. The theme under which the papers have been collected is Concurrency, Compositionality, and Correctness, reflecting the focus of Willem-Paul de Roever's research career. Topics addressed include model checking, computer science and state machines, ontology and mereology of domains, game theory, compiler correctness, fair scheduling and encryption algorithms.

Erste Untersuchungen der Halswirbelsäule werden stets mit Hilfe von Röntgenaufnahmen durchgeführt, und in den meisten Fällen genügen diese als Grundlage für die Diagnose. Mißbildungen, Tumoren, und noch öfter Traumata, Rheuma und sogar ganz gewöhnliche Nackenschmerzen erfordern eine radiologische Untersuchung der Wirbelsäule. Die Auswertung jedoch ist schwierig. Nimmt man einen Halswirbel in die Hand, so stellt man fest, um welch komplexes Gebilde es sich hierbei handelt. Bei radiologischen Aufnahmen wird die Auswertung noch durch die sich überlappenden Knochenteile, Anhäufungen und die verschiedenen Blickwinkel erschwert. Das Buch von J.-F. Bonneville und F. Cattin stellt eine originelle Interpretationsmethode von Röntgenaufnahmen vor, die die Auswertung wesentlich erleichtert. Dieses Buch zeigt, daß zwei- bzw. dreidimensionale Computertomogramme eine ausgezeichnete Hilfe zum Verständnis von konventionellen Röntgenbildern sein können. Der Leser bekommt gleichsam Zugang zu jedem Einzelteil des Knochens, und von da an wird alles einfach, Überlappungen verschwinden, die in der Röntgenaufnahme verborgenen Tücken werden sichtbar, die Anatomie triumphiert, das Bild lebt. Die Halswirbelsäule von J.-F. Bonneville und F. Cattin ist unentbehrlich für jeden Radiologen in seiner täglichen Praxis, aber ebenso auch für Chirurgen, Rheumatologen und Physiotherapeuten, die sich für die Halswirbelsäule interessieren.

All modern industries rely on large and complex software systems. In order to construct such large systems in a systematic manner, the focus of the development methodologies has switched in the last two decades from functional to structural issues. Formal methods have been applied successfully to the verification of medium-sized programs in protocol and hardware design. However, their application to the development of large systems requires a greater emphasis on specification, modeling, and validation techniques supporting the concepts of reusability and modifiability, and their implementation in new extensions of existing programming languages like Java. This state-of-the-art survey presents the outcome of the 7th Symposium on Formal Methods for Components and Objects, held in Sophia Antipolis, France, in October 2008. The volume contains 14 revised contributions submitted after the symposium by speakers from each of the following European IST projects: the IST-FP7 project COMPAS on compliance-driven models, languages, and architectures for services; the IST-FP6 project CREDO on modelling and analysis of evolutionary structures for distributed services; the IST-FP7 DEPLOY on industrial deployment of advanced system engineering methods for high productivity and dependability; the IST-FP6 project GridComp on grid programming with components; and the IST-FP6 project MOBIUS aiming at developing the technology for establishing trust and security for the next generation of global computers, using the proof carrying code paradigm.

The last few years have borne witness to a remarkable diversity of formal methods, with applications to sequential and concurrent software, to real-time and reactive systems, and to hardware design. In that time, many theoretical problems have been tackled and solved, and many continue to be worked upon. Yet it is by the suitability of their industrial application and the extent of their usage that formal methods will ultimately be judged. This volume presents the proceedings of the first international symposium of Formal Methods Europe, FME'93. The symposium focuses on the application of industrial-strength formal methods. Authors address the difficulties of scaling their techniques up to industrial-sized problems, and their suitability in the workplace, and discuss techniques that are formal (that is, they have a mathematical basis) and that are industrially applicable. The volume has four parts: - Invited lectures, containing a lecture by Cliff B. Jones and a lecture by Antonio Cau and Willem-Paul de Roever; - Industrial usage reports, containing 6 reports; - Papers, containing 32 selected and refereedpapers; - Tool descriptions, containing 11 descriptions.

The Z notation is a language for expressing mathematical specifications of computing systems. By providing a formal semantics for Z, this book justifies the claim that Z is a precise specification language, and provides a standard framework for understanding Z specifications.

This illuminating textbook provides a concise review of the core concepts in mathematics essential to computer scientists. Emphasis is placed on the practical computing applications enabled by seemingly abstract mathematical ideas, presented within their historical context. The text spans a broad selection of key topics, ranging from the use of finite field theory to correct code and the role of number theory in cryptography, to the value of graph theory when modelling networks and the importance of formal methods for safety critical systems. This fully updated new edition has been expanded with a more comprehensive treatment of algorithms, logic, automata theory, model checking, software reliability and dependability, algebra, sequences and series, and mathematical induction. Topics and features: includes numerous pedagogical features, such as chapter-opening key topics, chapter introductions and summaries, review questions, and a glossary; describes the historical contributions of such prominent figures as Leibniz, Babbage, Boole, and von Neumann; introduces the fundamental mathematical concepts of sets, relations and functions, along with the basics of number theory, algebra, algorithms, and matrices; explores arithmetic and geometric sequences and series, mathematical induction and recursion, graph theory, computability and decidability, and automata theory; reviews the core issues of coding theory, language theory, software engineering, and software reliability, as well as formal methods and model checking; covers key topics on logic, from ancient Greek contributions to modern applications in AI, and discusses the nature of mathematical proof and theorem proving; presents a short introduction to probability and statistics, complex numbers and quaternions, and calculus. This engaging and easy-to-understand book will appeal to students of computer science wishing for an overview of the mathematics used in computing, and to mathematicians curious about how their subject is applied in the field of computer science. The book will also capture the interest of the motivated general reader.