Bøger i Cambridge Tracts in Theoretical Computer Science serien

This book, based on courses taught at universities and summer schools, provides a broad introduction to the subject; many exercises are included with their solutions.

Declarative programs consist of mathematical functions and relations and are amenable to formal specification and verification, since the methods of logic and proof can be applied to the programs in a well-defined manner. Here Dr Padawitz emphasizes verification based on logical inference rules, i.e. deduction (in contrast with model-theoretic approaches, deductive methods can be automated to some extent). His treatment of the subject differs from others in that he tries to capture the actual styles and applications of programming; neither too general with respect to the underlying logic, nor too restrictive for the practice of programming. He generalizes and unifies results from classical theorem-proving and term rewriting to provide proof methods tailored to declarative program synthesis and verification. Detailed examples accompany the development of the methods, whose use is supported by a documented prototyping system. The book can be used for graduate courses or as a reference for researchers in formal methods, theorem-proving and declarative languages.

This book discusses the connection between two areas of semantics, namely the semantics of databases and the semantics of natural language, and links them via a common view of the semantics of time. It is argued that a coherent theory of the semantics of time is an essential ingredient for the success of efforts to incorporate more 'real world' semantics into database models. This idea is a relatively recent concern of database research but it is receiving growing interest. The book begins with a discussion of database querying which motivates the use of the paradigm of Montague Semantics and discusses the details of the intensional logic ILs. This is followed by a description of the author's own model, the Historical Relational Data Model (HRDM) which extends the RDM to include a temporal dimension. Finally the database querying language QEHIII is defined and examples illustrate its use. A formal model for the interpretation of questions is presented in this work which will form the basis for much further research.

This text for graduate students and researchers gives a complete coverage of the field with mathematical rigour, from basics to advanced topics. It closes the gap between theory and real practice by providing full proofs and executable code for all algorithms, showcasing the efficient and elegant solutions that finite-state methods offer.

This book is devoted to providing an accessible, unified and self-contained introduction to domain theory. It can be, and has been, used as an introductory textbook or as a general reference for professionals in computer science and logic.

Chaitin, the inventor of algorithmic information theory, presents in this book the strongest possible version of Goedel's incompleteness theorem, using an information theoretic approach based on the size of computer programs.

Graduate text in formal methods in computer science.

This 1991 book gives an overview of different areas of research in nonmonotonic reasoning. The guiding principles are: clarification of the different research activities in the area and appreciation of the fact that these research activities often represent different means to the same ends, namely sound theoretical foundations and efficient computation.

This book combines traditional graph theory with the matroid view of graphs in order to throw light on the mathematical approach to network analysis. The authors include many new results as well as synthesising and reworking much research done over the last 30 years.

In this book is presented the theoretical foundation of a higher-order logic programming language with equality, based on the clausal theory of types.

Many different structured methodologies exist, each employing a number of models and so a specification must be converted from one form to another during the development process. To solve this, Dr Tse proposes in this 1991 book a unifying framework behind popular structured models. He develops the frameworks and illustrates their practical usefulness.

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.

Artificial intelligence has recently turned to formal logic in the search for powerful yet well-behaved knowledge representation languages. This book, written for workers in artificial intelligence, covers the background of classical logic, including the major meta-theorems, and the state of the art in theorem proving, including Bibel's connection method.

The logic and methodology of design is examined in this book from the perspective of computer science. Computers provide the context for this both by discussion of the design process for hardware and software systems and by consideration of the role of computers in design in general. The question is whether we can construct a theory of design.

This 1993 book shows how formal logic can be used to specify the behaviour of hardware designs and reason about their correctness. The book is based in part on the author's own research as well as on graduate teaching. Thus it can be used to accompany courses on hardware verification and as a resource for research workers.

This book introduces and teaches the techniques of type theory by focusing on one particularly neat system and studying it in detail. In this way, all the key ideas are covered without getting involved in the complications of more advanced systems, but concentrating rather on the principles that make the theory work in practice.

The authors describe specification techniques from the unified view of the Common Object-oriented Language for Design.

The authors describe here a framework in which the type notation of functional languages is extended to include a distinguishing notation for run-times and compile-times. Consequently the ability to specify code and verify program correctness can be improved.

The author presents a theory whereby nets, terms and formulas represent concurrent processes at three levels of abstraction. The use of transformations in a series of case studies and the author identifies directions for research.

A complete account of the predicate transformation calculus semantics of sequential programs.

This 2001 book is an introduction to verifying concurrent programs scaling up to a realistic size. It is self-contained and comprehensive, guiding the reader from advanced undergraduate level. Every method is illustrated by examples, and a picture gallery of some of the subject's key figures complements the text.

This book describes the mathematical aspects of the semantics of programming languages. The main goals are to provide formal tools to assess the meaning of programming constructs in ways independent of both language and platform. To do this the authors explain denotational and operational semantics and exploit the duality between them.

The area of coalgebra has emerged within theoretical computer science with a unifying claim: to be the mathematics of computational dynamics. It combines ideas from the theory of dynamical systems and from the theory of state-based computation. Although still in its infancy, it is an active area of research that generates wide interest. Written by one of the founders of the field, this book acts as the first mature and accessible introduction to coalgebra. It provides clear mathematical explanations, with many examples and exercises involving deterministic and non-deterministic automata, transition systems, streams, Markov chains and weighted automata. The theory is expressed in the language of category theory, which provides the right abstraction to make the similarity and duality between algebra and coalgebra explicit, and which the reader is introduced to in a hands-on manner. The book will be useful to mathematicians and (theoretical) computer scientists and will also be of interest to mathematical physicists, biologists and economists.

This comprehensive text provides a modern and technically precise exposition of the fundamental theory and applications of temporal logics in computer science. Part I presents the basics of discrete transition systems, including constructions and behavioural equivalences. Part II examines the most important temporal logics for transition systems and Part III looks at their expressiveness and complexity. Finally, Part IV describes the main computational methods and decision procedures for model checking and model building - based on tableaux, automata and games - and discusses their relationships. The book contains a wealth of examples and exercises, as well as an extensive annotated bibliography. Thus, the book is not only a solid professional reference for researchers in the field but also a comprehensive graduate textbook that can be used for self-study as well as for teaching courses.

Rippling is a radically new technique for the automation of mathematical reasoning. It is widely applicable whenever a goal is to be proved from one or more syntactically similar givens. It was originally developed for inductive proofs, where the goal was the induction conclusion and the givens were the induction hypotheses. It has proved to be applicable to a much wider class of tasks, from summing series via analysis to general equational reasoning. The application to induction has especially important practical implications in the building of dependable IT systems, and provides solutions to issues such as the problem of combinatorial explosion. Rippling is the first of many new search control techniques based on formula annotation; some additional annotated reasoning techniques are also described here. This systematic and comprehensive introduction to rippling, and to the wider subject of automated inductive theorem proving, will be welcomed by researchers and graduate students alike.

Information is a central topic in computer science, cognitive science and philosophy. In spite of its importance in the 'information age', there is no consensus on what information is, what makes it possible, and what it means for one medium to carry information about another. Drawing on ideas from mathematics, computer science and philosophy, this book addresses the definition and place of information in society. The authors, observing that information flow is possible only within a connected distribution system, provide a mathematically rigorous, philosophically sound foundation for a science of information. They illustrate their theory by applying it to a wide range of phenomena, from file transfer to DNA, from quantum mechanics to speech act theory.

This is an advanced 2001 textbook on modal logic, a field which caught the attention of computer scientists in the late 1970s. Researchers in areas ranging from economics to computational linguistics have since realised its worth. The book is for novices and for more experienced readers, with two distinct tracks clearly signposted at the start of each chapter. The development is mathematical; prior acquaintance with first-order logic and its semantics is assumed, and familiarity with the basic mathematical notions of set theory is required. The authors focus on the use of modal languages as tools to analyze the properties of relational structures, including their algorithmic and algebraic aspects, and applications to issues in logic and computer science such as completeness, computability and complexity are considered. Three appendices supply basic background information and numerous exercises are provided. Ideal for anyone wanting to learn modern modal logic.

This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category theory; modal logic; linear logic; first-order arithmetic and second-order logic. In each case the aim is to illustrate the methods in relatively simple situations and then apply them elsewhere in much more complex settings. There are numerous exercises throughout the text. In general, the only prerequisite is a standard course in first-order logic, making the book ideal for graduate students and beginning researchers in mathematical logic, theoretical computer science and artificial intelligence. For the new edition, many sections have been rewritten to improve clarity, new sections have been added on cut elimination, and solutions to selected exercises have been included.

Nominal Sets gives a detailed account of this new approach to the syntax and semantics of programming languages based on symmetries of names. Covering theory and applications, the book will be welcomed by researchers and graduate students in theoretical computer science.

The is an introduction to simple type theory, exploring the relationship between proof and calculation. Each of its 52 sections ends with a set of exercises, some 200 in total. These are designed to help the reader get to grips with the subject. An appendix contains complete solutions to them.