This book principally concerns the rapidly growing area of what might be termed "Logical Complexity Theory": the study of bounded arithmetic, propositional proof systems, length of proof, and similar themes, and the relations of these topics to computational complexity theory. Issuing from a two-year international collaboration, the book contains articles concerning the existence of the most general unifier, a special case of Kreisel's conjecture on length-of-proof, propositional logic proof size, a new alternating logtime algorithm for boolean formula evaluation and relation to branching programs, interpretability between fragments of arithmetic, feasible interpretability, provability logic, open induction, Herbrand-type theorems, isomorphism between first and second order bounded arithmetics, forcing techniques in bounded arithmetic, and ordinal arithmetic in *L *D o. Also included is an extended abstract of J.P. Ressayre's new approach concerning the model completeness of the theory of real closed exponential fields. Additional features of the book include the transcription and translation of a recently discovered 1956 letter from Kurt Godel to J. von Neumann, asking about a polynomial time algorithm for the proof in k-symbols of predicate calculus formulas (equivalent to the P-NP question); and an open problem list consisting of seven fundamental and 39 technical questions contributed by many researchers, together with a bibliography of relevant references. This scholarly work will interest mathematical logicians, proof and recursion theorists, and researchers in computational complexity.

This book presents state-of-the-art research results in the area of formal methods for real-time and fault-tolerant systems. The papers consider problems and solutions in safety-critical system design and examine how wellthe use of formal techniques for design, analysis and verification serves in relating theory to practical realities. The book contains papers on real-time and fault-tolerance issues. Formal logic, process algebra, and action/event models are applied: - to specify and model qualitative and quantitative real-time and fault-tolerant behavior, - to analyze timeliness requirements and consequences of faulthypotheses, - to verify protocols and program code, - to formulate formal frameworks for development of real-time and fault-tolerant systems, - to formulate semantics of languages. The integration and cross-fertilization of real-time and fault-tolerance issues have brought newinsights in recent years, and these are presented in this book.

Attribute grammars have shown themselves to be a useful formalism for specifying the syntax and the static semantics of programming languages. They are also useful for implementing syntax-directed editors, compilers, translator writing systems and compiler generators, and any application that has a strong syntactic base. However, no textbooks are available that cover the entire field. To redress this imbalance, anInternational Summer School on Attribute Grammars, Applications and Systems was held in Prague, Czechoslovakia in June 1991. The course aimed at teaching the state of the art in attribute grammars, and their relation to other language specification methods. This volume presents the proceedings of the school. The papers are well suited for self-study, and a selection of them can be used for introductory courses in attribute grammars.

The workshop Computer Science Logic '90 was held at the Max-Planck-Haus in Heidelberg, Germany, October 1-5, 1990. It was the fourth in a series of worskhops, following CSL '89 at the University of Kaiserslautern (see LNCS 440), CSL '88 at the University of Duisberg (see LNCS 385), and CSL '87 at the University of Karlsruhe (see LNCS 329). This volume contains 24 papers, chosen by means of a review procedure from the 35 papers presented at the workshop, some of which were invited and some selected from a total of 89 submissions. The papers cover a wide range of topics arising from the applications of logic to computer science.

This volume contains the proceedings of the second workshop on Computer Aided Verification, held at DIMACS, Rutgers University, June 18-21, 1990. Itfeatures theoretical results that lead to new or more powerful verification methods. Among these are advances in the use of binary decision diagrams, dense time, reductions based upon partial order representations and proof-checking in controller verification. The motivation for holding a workshop on computer aided verification was to bring together work on effective algorithms or methodologies for formal verification - as distinguished, say, from attributes of logics or formal languages. The considerable interest generated by the first workshop, held in Grenoble, June 1989 (see LNCS 407), prompted this second meeting. The general focus of this volume is on the problem of making formal verification feasible for various models of computation. Specific emphasis is on models associated with distributed programs, protocols, and digital circuits. The general test of algorithm feasibility is to embed it into a verification tool, and exercise that tool on realistic examples: the workshop included sessionsfor the demonstration of new verification tools.

This volume contains the papers which have been accepted for presentation atthe Third International Symposium on Programming Language Implementation andLogic Programming (PLILP '91) held in Passau, Germany, August 26-28, 1991. The aim of the symposium was to explore new declarative concepts, methods and techniques relevant for the implementation of all kinds of programming languages, whether algorithmic or declarative ones. The intention was to gather researchers from the fields of algorithmic programming languages as well as logic, functional and object-oriented programming. This volume contains the two invited talks given at the symposium by H. Ait-Kaci and D.B. MacQueen, 32 selected papers, and abstracts of several system demonstrations. The proceedings of PLILP '88 and PLILP '90 are available as Lecture Notes in Computer Science Volumes 348 and 456.

This volume presents the papers selected for the Symposium Logic at Tver '92, held at Sokol, near Tver, Russia in July 1992. It is the second in a series of international symposia on logical foundations of computer science held in Russia. The meeting is a joint effort of scholars from both the former Soviet Union and the West, and indicates a new era of international cooperation. Sponsors of the meeting include: the Association for Computing Machinery, the Association for Symbolic Logic, andthe Committee on Mathematical Foundations of Computer Science of IEEE. The book is a unique source of information on the state of computer science research in the former Soviet Union and presents important discoveries in the area of logical foundations of computer science.

Number theory as studied by the logician is the subject matter of the book. This first volume can stand on its own as a somewhat unorthodox introduction to mathematical logic for undergraduates, dealing with the usual introductory material: recursion theory, first-order logic, completeness, incompleteness, and undecidability. In addition, its second chapter contains the most complete logical discussion of Diophantine Decision Problems available anywhere, taking the reader right up to the frontiers of research (yet remaining accessible to the undergraduate). The first and third chapters also offer greater depth and breadth in logico-arithmetical matters than can be found in existing logic texts. Each chapter contains numerous exercises, historical and other comments aimed at developing the student's perspective on the subject, and a partially annotated bibliography.

This volume contains papers presented at the first international workshop onword equations and related topics held at the University of T}bingen in October 1990. Word equations, the central topic of this annual workshop, lieat the intersection of several important areas of computer science, suchas unification theory, combinatorics on words, list processing, and constraint logic programming. The workshop is a forum where researchers fromthese different domains may present and discuss results and ideas, thereby supporting interaction and cross-fertilization between theoretical questions and practical applications. The volume collects papers which: - contain new and relevant results, - describe a new approach to a subject, or - give a survey of main developments in an area. Papers cover investigations on free groups, associative unification and Makanin's algorithm to decide the solvability of equations in free semigroups, general unification theory and its relationship to algebra and model theory, Thue systems, and finitely presented groups.

This book focuses on image based security techniques, namely visual cryptography, watermarking, and steganography. This book is divided into four sections. The first section explores basic to advanced concepts of visual cryptography. The second section of the book covers digital image watermarking including watermarking algorithms, frameworks for modeling watermarking systems, and the evaluation of watermarking techniques. The next section analyzes steganography and steganalysis, including the notion, terminology and building blocks of steganographic communication. The final section of the book describes the concept of hybrid approaches which includes all image-based security techniques. One can also explore various advanced research domains related to the multimedia security field in the final section. The book includes many examples and applications, as well as implementation using MATLAB, wherever required. Features: Provides a comprehensive introduction to visual cryptography, digital watermarking and steganography in one book Includes real-life examples and applications throughout Covers theoretical and practical concepts related to security of other multimedia objects using image based security techniques Presents the implementation of all important concepts in MATLAB

The courses given at the 1st C.I.M.E. Summer School of 1988 dealt with the main areas on the borderline between applied logic and theoretical computer science. These courses are recorded here in five expository papers: S. Homer: The Isomorphism Conjecture and its Generalization.- A. Nerode: Some Lectures on Intuitionistic Logic.- R.A. Platek: Making Computers Safe for the World. An Introduction to Proofs of Programs. Part I. - G.E. Sacks: Prolog Programming.- A. Scedrov: A Guide to Polymorphic Types.

These proceedings contain research and survey papers from many subfields of recursion theory, with emphasis on degree theory, in particular the development of frameworks for current techniques in this field. Other topics covered include computational complexity theory, generalized recursion theory, proof theoretic questions in recursion theory, and recursive mathematics.

This volume contains several invited papers as well as a selection of the other contributions. The conference was the first meeting of the Soviet logicians interested in com- puter science with their Western counterparts. The papers report new results and techniques in applications of deductive systems, deductive program synthesis and analysis, computer experiments in logic related fields, theorem proving and logic programming. It provides access to intensive work on computer logic both in the USSR and in Western countries.

This volume contains the papers presented at the International Scientific Symposium "Natural Language and Logic" held in Hamburg in May 1989. The aim of the papers is to present and discuss latest developments in the application of logic-based meth- ods for natural language understanding. Logic-based methods have gained in importance in the field of computational linguistics as well as for representing various types of knowledge in natural language understanding systems. The volume gives an overview of recent results achieved within the LILOG project (LInguistic and LOgic methods for understanding German texts) - one of the largest research projects in the field of text understanding - as well as within related natural language understanding systems.

The volume contains the proceedings of the 16th Spring School on Theoretical Computer Science held in Ramatuelle, France, in May 1988. It is a unique combination of research level articles on various aspects of the theory of finite automata and its applications. Advances made in the last five years on the mathematical foundations form the first part of the book. The second part is devoted to the important problems of the theory including star-height, concatenation hierarchies, and connections with logic and word problems. The last part presents a large variety of possible applications: number theory, distributed systems, algorithms on strings, theory of codes, complexity of boolean circuits and others.

These proceedings include the papers presented at the logic meeting held at the Research Institute for Mathematical Sciences, Kyoto University, in the summer of 1987. The meeting mainly covered the current research in various areas of mathematical logic and its applications in Japan. Several lectures were also presented by logicians from other countries, who visited Japan in the summer of 1987.

The aim of this book is to reflect the substantial re- search done in Artificial Intelligence on sorts and types. The main contributions come from knowledge representation and theorem proving and important impulses come from the "application areas," i.e. natural language (understanding) systems, computational linguistics, and logic programming. The workshop brought together researchers from logic, theoretical computer science, theorem proving, knowledge representation, linguistics, logic programming and qualitative reasoning.

Rewriting has always played an important role in symbolic manipulation and automated deduction systems. The theory of rewriting is an outgrowth of Combinatory Logic and the Lambda Calculus. Applications cover broad areas in automated reasoning, programming language design, semantics, and implementations, and symbolic and algebraic manipulation. The proceedings of the third International Conference on Rewriting Techniques and Applications contain 34 regular papers, covering many diverse aspects of rewriting (including equational logic, decidability questions, term rewriting, congruence-class rewriting, string rewriting, conditional rewriting, graph rewriting, functional and logic programming languages, lazy and parallel implementations, termination issues, compilation techniques, completion procedures, unification and matching algorithms, deductive and inductive theorem proving, GrAbner bases, and program synthesis). It also contains 12 descriptions of implemented equational reasoning systems. Anyone interested in the latest advances in this fast growing area should read this volume.

Originally published in 1969. This book is for undergraduates whether specializing in philosophy or not. It assumes no previous knowledge of logic but aims to show how logical notions arise from, or are abstracted from, everyday discourse, whether technical or non-technical. It sets out a knowledge of principles and, while not historical, gives an account of the reasons for which modern systems have emerged from the traditional syllogistic logic, demonstrating how certain central ideas have developed. The text explains the connections between everyday reasoning and formal logic and works up to a brief sketch of systems of propositional calculus and predicate-calculus, using both the axiomatic method and the method of natural deduction. It provides a self-contained introduction but for those who intend to study the subject further it contains many suggestions and a sound basis for more advanced study.

Drawing on the authors' use of the Hadamard-related theory in several successful engineering projects, Theory and Applications of Higher-Dimensional Hadamard Matrices, Second Edition explores the applications and dimensions of Hadamard matrices. This edition contains a new section on the applications of higher-dimensional Hadamard matrices to the areas of telecommunications and information security. The first part of the book presents fast algorithms, updated constructions, existence results, and generalized forms for Walsh and Hadamard matrices. The second section smoothly transitions from two-dimensional cases to three-, four-, and six-dimensional Walsh and Hadamard matrices and transforms. In the third part, the authors discuss how the n-dimensional Hadamard matrices of order 2 are applied to feed-forward networking, stream ciphers, bent functions, and error correcting codes. They also cover the Boolean approach of Hadamard matrices. The final part provides examples of applications of Hadamard-related ideas to the design and analysis of one-dimensional sequences and two-dimensional arrays. The theory and ideas of Hadamard matrices can be used in many areas of communications and information security. Through the research problems found in this book, readers can further explore the fascinating issues and applications of the theory of higher-dimensional Hadamard matrices.

The papers collected in this volume are most of the material presented at the Advanced School on Mathematical Models for the Semantics of Parallelism, held in Rome, September 24- October 1, 1986. The need for a comprehensive and clear presentation of the several semantical approaches to parallelism motivated the stress on mathematical models, by means of which comparisons among different approaches can also be performed in a perspicuous way.

This book provides an introduction to the theory of existentially closed groups, for both graduate students and established mathematicians. It is presented from a group theoretical, rather than a model theoretical, point of view. The recursive function theory that is needed is included in the text. Interest in existentially closed groups first developed in the 1950s. This book brings together a large number of results proved since then, as well as introducing new ideas, interpretations and proofs. The authors begin by defining existentially closed groups, and summarizing some of the techniques that are basic to infinite group theory (e.g. the formation of free products with amalgamation and HNN-extensions). From this basis the theory is developed and many of the more recently discovered results are proved and discussed. The aim is to assist group theorists to find their way into a corner of their subject which has its own characteristic flavour, but which is recognizably group theory.