1 In a number of recent presentations – most notably at FME’96 –oneofthe foremost scientists in the ?eld of formal methods, C.A.R. Hoare,has highlighted the fact that formal methods are not the only technique for producing reliable software. This seems to have caused some controversy,not least amongst formal methods practitioners. How can one of the founding fathers of formal methods seemingly denounce the ?eld of research after over a quarter of a century of support? This is a question that has been posed recently by some formal methods skeptics. However, Prof. Hoare has not abandoned formal methods. He is reiterating, 2 albeitmoreradically,his1987view thatmorethanonetoolandnotationwillbe requiredinthepractical,industrialdevelopmentoflarge-scalecomplexcomputer systems; and not all of these tools and notations will be, or even need be, formal in nature. Formalmethods arenotasolution,butratheroneofaselectionoftechniques that have proven to be useful in the development of reliable complex systems, and to result in hardware and software systems that can be produced on-time and within a budget, while satisfying the stated requirements. After almostthree decades,the time has come to view formalmethods in the context of overall industrial-scale system development, and their relationship to othertechniquesandmethods.Weshouldnolongerconsidertheissueofwhether we are “pro-formal” or “anti-formal”, but rather the degree of formality (if any) that we need to support in system development. This is a goal of ZUM’98, the 11th International Conference of Z Users, held for the ?rst time within continental Europe in the city of Berlin, Germany.

This book constitutes the refereed proceedings of the Second International Conference of B and Z Users, ZB 2002, held in Grenoble, France in January 2002. The 24 papers presented together with three invited contributions were carefully reviewed and selected for inclusion in the book. The book documents the recent advances for the Z formal specification notion and for the B method; the full scope is covered, ranging from foundational and theoretical issues to advanced applications, tools, and case studies.

The refereed proceedings of the Third International Conference of Z and B Users, ZB 2003, held in Turku, Finland in June 2003. The 28 revised full papers presented together with 3 invited papers were carefully reviewed and selected for inclusion in the book. The book documents the recent advances for the Z formal specification notation and for the B method, spanning the full scope from foundational, theoretical, and methodological issues to advanced applications, tools, and case studies.

Formal methods are coming of age. Mathematical techniques and tools are now regarded as an important part of the development process in a wide range of industrial and governmental organisations. A transfer of technology into the mainstream of systems development is slowly, but surely, taking place. FM’99, the First World Congress on Formal Methods in the Development of Computing Systems, is a result, and a measure, of this new-found maturity. It brings an impressive array of industrial and applications-oriented papers that show how formal methods have been used to tackle real problems. These proceedings are a record of the technical symposium ofFM’99:alo- side the papers describingapplicationsofformalmethods,youwill ndtechnical reports,papers,andabstracts detailing new advances in formaltechniques,from mathematical foundations to practical tools. The World Congress is the successor to the four Formal Methods Europe Symposia, which in turn succeeded the four VDM Europe Symposia. This s- cession re?ects an increasing openness within the international community of researchers and practitioners: papers were submitted covering a wide variety of formal methods and application areas. The programmecommittee re?ects the Congress’s international nature, with a membership of 84 leading researchersfrom 38 di erent countries.The comm- tee was divided into 19 tracks, each with its own chair to oversee the reviewing process. Our collective task was a di cult one: there were 259 high-quality s- missions from 35 di erent countries.

It is not an exaggeration to view Professor Lee's book," Software Engineer ing with Computational Intelligence," or SECI for short, as a pioneering contribution to software engineering. Breaking with the tradition of treat ing uncertainty, imprecision, fuzziness and vagueness as issues of peripheral importance, SECI moves them much closer to the center of the stage. It is ob vious, though still not widely accepted, that this is where these issues should be, since the real world is much too complex and much too ill-defined to lend itself to categorical analysis in the Cartesian spirit. As its title suggests, SECI employs the machineries of computational intel ligence (CI) and, more or less equivalently, soft computing (SC), to deal with the foundations and principal issues in software engineering. Basically, CI and SC are consortia of methodologies which collectively provide a body of con cepts and techniques for conception, design, construction and utilization of intelligent systems. The principal constituents of CI and SC are fuzzy logic, neurocomputing, evolutionary computing, probabilistic computing, chaotic computing and machine learning. The leitmotif of CI and SC is that, in general, better performance can be achieved by employing the constituent methodologies of CI and SC in combination rat her than in a stand-alone mode. In what follows, I will take the liberty of focusing my attention on fuzzy logic and fuzzy set theory, and on their roles in software engineering. But first, a couple of points of semantics which are in need of clarification.

Refinement is one of the cornerstones of the formal approach to software engineering, and its use in various domains has led to research on new applications and generalisation. This book brings together this important research in one volume, with the addition of examples drawn from different application areas. It covers four main themes: Data refinement and its application to Z Generalisations of refinement that change the interface and atomicity of operations Refinement in Object-Z Modelling state and behaviour by combining Object-Z with CSP Refinement in Z and Object-Z: Foundations and Advanced Applications provides an invaluable overview of recent research for academic and industrial researchers, lecturers teaching formal specification and development, industrial practitioners using formal methods in their work, and postgraduate and advanced undergraduate students. This second edition is a comprehensive update to the first and includes the following new material: Early chapters have been extended to also include trace refinement, based directly on partial relations rather than through totalisation Provides an updated discussion on divergence, non-atomic refinements and approximate refinement Includes a discussion of the differing semantics of operations and outputs and how they affect the abstraction of models written using Object-Z and CSP Presents a fuller account of the relationship between relational refinement and various models of refinement in CSP Bibliographic notes at the end of each chapter have been extended with the most up to date citations and research

This volume contains the lecture notes of the five courses and one seminar given at the School on Engineering Trustworthy Software Systems (SETSS 2014), held in September 2014 at Southwest University in Chongqing, China. The material is useful for postgraduate students, researchers, academics and industrial engineers who are interested in the theory and practice of methods and tools for the design and programming of trustworthy software systems. The common themes of the courses include the design and use of theories, techniques and tools for software specification and modeling, analysis and verification. The courses cover sequential programming, component- and object software, hybrid systems and cyber-physical systems with challenges of termination, security, safety, security, fault-tolerance and real-time requirements. The techniques include model checking, correctness by construction through refinement and model transformations, synthesis and computer algebra.

Formal methods have been established as the rigorous engineering methodology for the system development. Applying formal methods to a large and complex system development often requires the modelling of different aspects of such a system. For instance, complex systems (such as integrated avionics systems, engine control software) can involve functional and timing requirements that must be eventually implemented as executing code on a communicating distributed topology. This book contains the papers presented at the First International Workshop on Integrated Formal Methods, held at the University of York in June 1999. The conference provided a forum for the discussion of theoretical aspects of combing behavioural and state-based formalisms and practical solutions to the industrial problems of this approach.

This volume contains the proceedings of MPC 2000, the ?fth international c- ference on Mathematics of Program Construction. This series of conferences aims to promote the development of mathematical principles and techniques that are demonstrably useful and usable in the process of constructing c- puter programs (whether implemented in hardware or software). The focus is on techniques that combine precision with concision, enabling programs to be constructed by formal calculation. Within this theme, the scope of the series is very diverse, including programming methodology, program speci?cation and transformation, programming paradigms, programming calculi, and progr- ming language semantics. The quality of the papers submitted to the conference was in general very high. However,the number of submissions has decreased compared to the pre- ous conferences in the series. Each paper was refereed by at least ?ve and often more committee members. In order to maintain the high standards of the c- ference the committee took a stringent view on quality; this has meant that, in some cases, a paper was rejected even though there was a basis for a good c- ference or journal paper but the submitted paper did not meet the committee’s required standards. In a few cases a good paper was rejected on the grounds that it did not ?t within the scope of the conference.