Hardware and software systems will inevitably grow in scale and functionality. Because of this increase in complexity, the likelihood of subtle errors is much greater. Moreover, some of these errors may cause catastrophic loss of money, time, or even human life. A major goal of software engineering is to enable developers to construct systems that operate reliably despite this complexity. One way of achieving this goal is by using formal methods, which are mathematically based languages, techniques, and tools for specifying and verifying such systems. Use of formal methods does not a priori guarantee correctness. However, they can greatly increase our understanding of a system by revealing inconsistencies, ambiguities, and incompleteness that might otherwise go undetected. The first part of this report assesses the state of the art in specification and verification. For verification, we highlight advances in model checking and theorem proving. In the three sections on specification, model checking, and theorem proving, we explain what we mean by the general technique and briefly describe some successful case studies and well-known tools. The second part of this report outlines future directions in fundamental concepts, new methods and tools, integration of methods, and education and technology transfer. We close with summary remarks and pointers to resources for more information.

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Formal methods: state of the art and future directions

Formal methods used in developing computer systems (i.e. mathematically based techniques for describing system properties) are defined, and their role is delineated. Formal specification languages, which provide the formal method's mathematical basis, are examined. Certain pragmatic concerns about formal methods and their users, uses, and characteristics are discussed. Six well-known or commonly used formal methods are illustrated by simple examples. They are Z, VDM, Larch, temporal logic, CSP, and transition axioms. >

A specifier's introduction to formal methods

Formal methods and testing are two important approaches that assist in the development of high-quality software. While traditionally these approaches have been seen as rivals, in recent years a new consensus has developed in which they are seen as complementary. This article reviews the state of the art regarding ways in which the presence of a formal specification can be used to assist testing.

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Using formal specifications to support testing

The emergence of the UML as a de facto standard for object-oriented modeling has been mirrored by the success of the B method as a practically useful formal modeling technique The two notations have much to offer each other The UML provides an accessible visualization of models facilitating communication of ideas but lacks formal precise semantics B, on the other hand, has the precision to support animation and rigorous verification but requires significant effort in training to overcome the mathematical barrier that many practitioners perceive We utilize a derivation of the B notation as an action and constraint language for the UML and define the semantics of UML entities via a translation into B Through the UML-B profile we provide specializations of UML entities to support model refinement The result is a formally precise variant of UML that can be used for refinement based, object-oriented behavioral modeling The design of UML-B has been guided by industrial applications

UML-B: Formal modeling and design aided by UML

Digital libraries (DLs) are complex information systems and therefore demand formal foundations lest development efforts diverge and interoperability suffers. In this article, we propose the fundamental abstractions of Streams, Structures, Spaces, Scenarios, and Societies (5S), which allow us to define digital libraries rigorously and usefully. Streams are sequences of arbitrary items used to describe both static and dynamic (e.g., video) content. Structures can be viewed as labeled directed graphs, which impose organization. Spaces are sets with operations on those sets that obey certain constraints. Scenarios consist of sequences of events or actions that modify states of a computation in order to accomplish a functional requirement. Societies are sets of entities and activities and the relationships among them. Together these abstractions provide a formal foundation to define, relate, and unify concepts---among others, of digital objects, metadata, collections, and services---required to formalize and elucidate "digital libraries". The applicability, versatility, and unifying power of the 5S model are demonstrated through its use in three distinct applications: building and interpretation of a DL taxonomy, informal and formal analysis of case studies of digital libraries (NDLTD and OAI), and utilization as a formal basis for a DL description language.

Streams, structures, spaces, scenarios, societies (5s): A formal model for digital libraries

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. It makes a detailed theoretical comparison between schemas, the Z construct for breaking specifications into modules, and the analogous facilities in other languages such as CLEAR and ASL. The final chapter contains a number of studies in Z style, showing that Z can be used for a wide variety of specification tasks.

J. M. Spivey

Papers

Understanding Z: A Specification Language and its Formal Semantics