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  3. Cambridge Tracts in Theoretical Computer Science

This series offers books on theoretical computer science, that part of computer science concerned with fundamental mathematical questions about computers, programs, algorithms, data, and information processing systems in general. Computers and programs are inherently mathematical objects, and an understanding of their mathematical basis is essential to the appreciation of the foundations of computer science.The series covers the complete field of theoretical computer science, including mathematical foundations of computer science, formal methods of reasoning about programs and data, and formal semantics of programs and data, including formal semantics for natural language, pictures, and sound.

  • Associate Editors: S. Abramsky, Oxford University
  • Editorial Boards: P. H. Aczel, University of Manchester, Y. Gurevich, Microsoft Research, J. V. Tucker, Swansea University

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43 results in Cambridge Tracts in Theoretical Computer Science

Page 2 of 3

A Unifying Framework for Structured Analysis and Design Models
  • An Approach Using Initial Algebra Semantics and Category Theory
  • T. H. Tse
  • Published online:
    28 January 2010
    Print publication:
    09 May 1991
  • Structured methodologies are a popular and powerful tool in information systems development. Many different ones 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 problem, Dr Tse proposes in this 1991 book a unifying framework behind popular structured models. He approaches the problem from the viewpoints of algebra and category theory. He not only develops the frameworks but also illustrates their practical and theoretical usefulness. Thus this book will provide insight for software engineers into how methodologies can be formalised and will open up a range of applications and problems for theoretical computer scientists.

Higher Order Logic and Hardware Verification
  • T. F. Melham
  • Published online:
    21 January 2010
    Print publication:
    11 November 1993
  • This 1993 book shows how formal logic can be used to specify the behaviour of hardware designs and reason about their correctness. A primary theme of the book is the use of abstraction in hardware specification and verification. The author describes how certain fundamental abstraction mechanisms for hardware verification can be formalised in logic and used to express assertions about design correctness and the relative accuracy of models of hardware behaviour. His approach is pragmatic and driven by examples. He also includes an introduction to higher-order logic, which is a widely used formalism in this subject, and describes how that formalism is actually used for hardware verification. 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.

Action Semantics
  • Peter D. Mosses
  • Published online:
    19 January 2010
    Print publication:
    13 August 1992
  • Action Semantics is a novel approach to the formal description of programming languages. Its abstractness is at an intermediate level, between that of denotational and operational semantics. Action Semantics has considerable pragmatic advantages over all previous approaches, in its comprehensibility and accessibility, and especially in the usefulness of its semantic descriptions of realistic programming languages. In this volume, Dr Peter Mosses gives a thorough introduction to action semantics, and provides substantial illustrations of its use. Graduates of computer science or maths who have an interest in the semantics of programming languages will find Action Semantics a most helpful book.

The Clausal Theory of Types
  • D. A. Wolfram
  • Published online:
    12 January 2010
    Print publication:
    22 April 1993
  • Logic programming was based on first-order logic. Higher-order logics can also lead to theories of theorem-proving. This book introduces just such a theory, based on a lambda-calculus formulation of a clausal logic with equality, known as the Clausal Theory of Types. By restricting this logic to Horn clauses, a concise form of logic programming that incorporates functional programming is achieved. The book begins by reviewing the fundamental Skolem-Herbrand-Gödel Theorem and resolution, which are then extrapolated to a higher-order setting; this requires introducing higher-order equational unification which builds in higher-order equational theories and uses higher-order rewriting. The logic programming language derived has the unique property of being sound and complete with respect to Henkin-Andrews general models, and consequently of treating equivalent terms as identical. First published in 1993, the book can be used for graduate courses in theorem-proving, but will be of interest to all working in declarative programming.

Process Algebra
  • J. C. M. Baeten, W. P. Weijland
  • Published online:
    08 January 2010
    Print publication:
    25 October 1990
  • This is an introduction to process algebra, also known as the Algebra of Communicating Processes (ACP). It is a self-contained mathematical approach to the theory which can be used for graduate courses, though it also has material of interest to researchers. It is a unique introduction to this model of concurrent programming and will be essential reading for all computer scientists interested in parallel processing and algebraic methods in computer science.

Predicate Transformer Semantics
  • Ernest. G. Manes
  • Published online:
    06 January 2010
    Print publication:
    13 August 1992
  • A central problem in the design of programming systems is to provide methods for verifying that computer code performs to specification. This book presents a rigorous foundation for defining Boolean categories, in which the relationship between specification and behaviour can be explored. Boolean categories provide a rich interface between program constructs and techniques familiar from algebra, for instance matrix- or ideal-theoretic methods. The book's distinction is that the approach relies on only a single program construct (the first-order theory of categories), the others being derived mathematically from four axioms. Development of these axioms (which are obeyed by an abundance of program paradigms) yields Boolean algebras of 'predicates', loop-free constructs, and a calculus of partial and total correctness which is shown to be the standard one of Hoare, Dijkstra, Pratt, and Kozen. The book is based in part on courses taught by the author, and will appeal to graduate students and researchers in theoretical computer science.

Nets, Terms and Formulas
  • Three Views of Concurrent Processes and their Relationship
  • E. -R. Olderog
  • Published online:
    06 January 2010
    Print publication:
    03 October 1991
  • The author presents a theory of concurrent processes where three different semantic description methods that are usually studied in isolation are brought together. Petri nets describe processes as concurrent and interacting machines; algebraic process terms describe processes as abstract concurrent processes; and logical formulas specify the intended communication behaviour of processes. At the heart of this theory are two sets of transformation rules for the top-down design of concurrent processes. The first set can be used to transform stepwise logical formulas into process terms, whilst process terms can be transformed into Petri nets by the second set. These rules are based on novel techniques for the operational and denotational semantics of concurrent processes. Various results and relationships between nets, terms and formulas starting with formulas and illustrated by examples. The use of transformations is demonstrated in a series of case studies, and the author also identifies directions for research.

Applications of Process Algebra
  • Edited by J. C. M. Baeten
  • Published online:
    03 December 2009
    Print publication:
    20 September 1990
  • This book gives applications of the theory of process algebra, or Algebra of Communicating Processes (ACP), that is the study of concurrent or communicating processes studied using an algebraic framework. The approach is axiomatic; the authors consider structures that are some set of mostly equational axioms, which are equipped with several operators. Thus the term 'algebra' is used in the model-theoretic sense. The axiomatic approach enables one to organize the field of process theories. The theory is applied systematically to a number of situations, including systolic algorithms, semantics of an object-oriented language, and protocols. It will be welcomed by computer scientists working in parallel programming.

Basic Simple Type Theory
  • J. Roger Hindley
  • Published online:
    02 December 2009
    Print publication:
    31 July 1997
  • Type theory is one of the most important tools in the design of higher-level programming languages, such as ML. This book introduces and teaches its techniques 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. This book takes a type-assignment approach to type theory, and the system considered is the simplest polymorphic one. The author covers all the basic ideas, including the system's relation to propositional logic, and gives a careful treatment of the type-checking algorithm which lies at the heart of every such system. Also featured are two other interesting algorithms that have been buried in inaccessible technical literature. The mathematical presentation is rigorous but clear, making the book at a level which can be used as an introduction to type theory for computer scientists.

Algorithmic Information Theory
  • Gregory. J. Chaitin
  • Published online:
    23 November 2009
    Print publication:
    15 October 1987
  • Chaitin, the inventor of algorithmic information theory, presents in this book the strongest possible version of Gödel's incompleteness theorem, using an information theoretic approach based on the size of computer programs. One half of the book is concerned with studying the halting probability of a universal computer if its program is chosen by tossing a coin. The other half is concerned with encoding the halting probability as an algebraic equation in integers, a so-called exponential diophantine equation.

Epistemic Logic for AI and Computer Science
  • J.-J. Ch. Meyer, W. van der Hoek
  • Published online:
    11 November 2009
    Print publication:
    24 November 1995
  • Epistemic logic has grown from its philosophical beginnings to find diverse applications in computer science as a means of reasoning about the knowledge and belief of agents. This book, based on courses taught at universities and summer schools, provides a broad introduction to the subject; many exercises are included together with their solutions. The authors begin by presenting the necessary apparatus from mathematics and logic, including Kripke semantics and the well-known modal logics K, T, S4 and S5. Then they turn to applications in the contexts of distributed systems and artificial intelligence: topics that are addressed include the notions of common knowledge, distributed knowledge, explicit and implicit belief, the interplays between knowledge and time, and knowledge and action, as well as a graded (or numerical) variant of the epistemic operators. The problem of logical omniscience is also discussed extensively. Halpern and Moses' theory of honest formulae is covered, and a digression is made into the realm of non-monotonic reasoning and preferential entailment. Moore's autoepistemic logic is discussed, together with Levesque's related logic of 'all I know'. Furthermore, it is shown how one can base default and counterfactual reasoning on epistemic logic.

Theoretical Foundations of VLSI Design
  • Edited by K. McEvoy, J. V. Tucker
  • Published online:
    06 November 2009
    Print publication:
    13 December 1990
  • This book discusses recent research in the theoretical foundations of several subjects of importance for the design of hardware, and for computer science in general. The physical technologies of very large scale integration (VLSI) are having major effects on the electronic industry. The potential diversity and complexity of digital systems have begun a revolution in the technologies of digital design, involving the application of concepts and methods to do with algorithms and programming. In return, the problems of VLSI design have led to new subjects becoming of importance in computer science. Topics covered in this volume include: models of VLSI complexity; complexity theory; systolic algorithm design; specification theory; verification theory; design by stepwise refinement and transformations. A thorough literature survey with an exhaustive bibliography is also included. The book has grown from a workshop held at the Centre for Theoretical Computer Science at Leeds University and organised by the editors.

Formal Specification and Design
  • L. M. G. Feijs, H. B. M. Jonkers
  • Published online:
    02 November 2009
    Print publication:
    22 October 1992
  • Formal specification is a method for precisely modelling computer-based systems that combines concepts from software engineering and mathematical logic. In this book the authors describe algebraic and state-based specification techniques from the unified view of the Common Object-oriented Language for Design, COLD, a wide-spectrum language in the tradition of VDM and Z. The kernel language is explained in detail, with many examples, including: set representation, a display device, an INGRES-like database system, and a line editor. Fundamental techniques such as initial algebra semantics, loose semantics, partial functions, hiding, sharing, predicate and dynamic logic, abstraction functions, representation of invariants and black-box correctness are also presented. More advanced ideas, for example Horn logic, and large systems are given in the final part. Appendices contain full details of the language's syntax and a specification library. Techniques for software development and design are emphasised throughout, so the book will be an excellent choice for courses in these areas.

The Uncertain Reasoner's Companion
  • A Mathematical Perspective
  • J. B. Paris
  • Published online:
    29 October 2009
    Print publication:
    12 January 1995
  • Reasoning under uncertainty, that is, making judgements with only partial knowledge, is a major theme in artificial intelligence. Professor Paris provides here an introduction to the mathematical foundations of the subject. It is suited for readers with some knowledge of undergraduate mathematics but is otherwise self-contained, collecting together the key results on the subject and formalizing within a unified framework the main contemporary approaches and assumptions. The author has concentrated on giving clear mathematical formulations, analyses, justifications and consequences of the main theories about uncertain reasoning, so the book can serve as a textbook for beginners or as a starting point for further basic research into the subject. It will be welcomed by graduate students and research workers in logic, philosophy and computer science as an account of how mathematics and artificial intelligence can complement and enrich each other.

Deductive and Declarative Programming
  • Peter Padawitz
  • Published online:
    24 October 2009
    Print publication:
    22 October 1992
  • 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.

Free Choice Petri Nets
  • Jorg Desel, Javier Esparza
  • Published online:
    21 October 2009
    Print publication:
    12 January 1995
  • Petri nets are a popular and powerful formal model for the analysis and modelling of concurrent systems, and a rich theory has developed around them. Petri nets are taught to undergraduates, and also used by industrial practitioners. This book focuses on a particular class of petri nets, free choice petri nets, which play a central role in the theory. The text is very clearly organised, with every notion carefully explained and every result proved. Clear exposition is given for place invariants, siphons, traps and many other important analysis techniques. The material is organised along the lines of a course book, and each chapter contains numerous exercises, making this book ideal for graduate students and research workers alike.

Metamathematics, Machines and Gödel's Proof
  • N. Shankar
  • Published online:
    16 October 2009
    Print publication:
    12 May 1994
  • Mathematicians from Leibniz to Hilbert have sought to mechanise the verification of mathematical proofs. Developments arising out of Gödel's proof of his incompleteness theorem showed that no computer program could automatically prove true all the theorems of mathematics. In practice, however, there are a number of sophisticated automated reasoning programs that are quite effective at checking mathematical proofs. Now in paperback, this book describes the use of a computer program to check the proofs of several celebrated theorems in metamathematics including Gödel's incompleteness theorem and the Church–Rosser theorem. The computer verification using the Boyer–Moore theorem prover yields precise and rigorous proofs of these difficult theorems. It also demonstrates the range and power of automated proof checking technology. The mechanisation of metamathematics itself has important implications for automated reasoning since metatheorems can be applied by labour-saving devices to simplify proof construction. The book should be accessible to scientists and philosophers with some knowledge of logic and computing.

The Logic of Typed Feature Structures
  • With Applications to Unification Grammars, Logic Programs and Constraint Resolution
  • Robert L. Carpenter
  • Published online:
    12 October 2009
    Print publication:
    26 June 1992
  • This book develops the theory of typed feature structures, a data structure that generalizes both first-order terms and feature structures of unification-based grammars to include inheritance, typing, inequality, cycles and intensionality. The resulting synthesis serves as a logical foundation for grammars, logic programming and constraint-based reasoning systems. A logical perspective is adopted which employs an attribute-value description language along with complete equational axiomatizations of the various systems of feature structures. At the same time, efficiency concerns are kept in mind and complexity and representability results are provided. The application of feature structures to phrase structure grammars is described and completeness results are shown for standard evaluation strategies. Definite clause logic programs are treated as a special case of phrase structure grammars. Constraint systems are introduced and an enumeration technique is developed for solving arbitrary attribute-value logic constraints. This book, with its innovative approach to data structure, will be essential reading for researchers in computational linguistics, logic programming and knowledge representation. Its self-contained presentation makes it flexible enough to serve as both a research tool and a text book.

Two-Level Functional Languages
  • Flemming Nielson, Hanne Riis Nielson
  • Published online:
    12 October 2009
    Print publication:
    16 July 1992
  • The authors describe here a framework in which the type notation of functional languages is extended to include a notation for binding times (that is run-time and compile-time) that distinguishes between them. Consequently the ability to specify code and verify program correctness can be improved. Two developments are needed, the first of which introduces the binding time distinction into the lambda calculus, in a manner analogous with the introduction of types into the untyped lambda calculus. Methods are also presented for introducing combinators for run-time. The second concerns the interpretation of the resulting language, which is known as the mixed lambda-calculus and combinatory logic. The notion of 'parametrized semantics' is used to describe code generation and abstract interpretation. The code generation is for a simple abstract machine designed for the purpose; it is close to the categorical abstract machine. The abstract interpretation focuses on a strictness analysis that generalises Wadler's analysis for lists.

Formal Semantics and Pragmatics for Natural Language Querying
  • James Clifford
  • Published online:
    06 October 2009
    Print publication:
    29 June 1990
  • 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.

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