About this product

Product Identifiers

PublisherDover Publications, Incorporated

ISBN-100486614719

ISBN-139780486614717

eBay Product ID (ePID)127387046

Product Key Features

Number of Pages288 Pages

Publication NameComputability and Unsolvability

LanguageEnglish

Publication Year1985

SubjectLogic

TypeTextbook

Subject AreaMathematics

AuthorMartin Davis

SeriesDover Books on Computer Science Ser.

FormatTrade Paperback

Dimensions

Item Height0.6 in

Item Weight12.1 Oz

Item Length8.5 in

Item Width5.4 in

Additional Product Features

Intended AudienceCollege Audience

LCCN82-007287

Dewey Edition19

Dewey Decimal517.5

Table Of ContentPreface to the Dover Edition; Preface to the First Edition; Glossary of special symbols Introduction 1. Heuristic Remarks on Decision Problems 2. Suggestions to the Reader 3. Notational Conventions Part 1. The general theory of computability Chapter 1. Computable Functions 1. Turing Machines 2. Computable Functions and Partially Computable functions 3. Some Examples 4. Relatively Computable functions Chapter 2. Operations on Computable Functions 1. Preliminary Lemmas 2. Composition and Minimalization Chapter 3. Recursive functions 1. Some Classes of Functions 2. Finite Sequences of Natural Numbers 3. Primitive Recursion 4. Primitive Recursive functions 5. Recursive Sets and Predicates Chapter 4. Turing Machines Self-applied 1. Arithmetization of the Theory of Turing Machines 2. Computability and Recursiveness 3. A Universal Turing Machine Chapter 5. Unsolvable Decision Problems 1. Semicomputable Predicates 2. Decision Problems 3. Properties of Semicomputable Predicates 4. Recursively enumerable Sets 5. Two Recursively enumerable Sets 6. A Set Which Is Not Recursively Enumerable Part 2. Applications of the General Theory Chapter 6. Combinatorial Problems 1. Combinatorial systems 2. Turing machines and Semi-Thue Systems 3. Thue Systems 4. The Word Problem for Semigroups 5. Normal Systems and Post Systems Chapter 7. Diophantine Equations 1. Hilbert's Tenth Problem 2. Arithmetical and Diophantine Predicates 3. Arithmetical Representation of Semicomputable Predicates Chapter 8. Mathematical Logic 1. Logics 2. Incompleteness and Unsolvability Theorems for Logics 3. Arithmetical Logics 4. First-order Logics 5. Partial Propositional Calculi Part 3. Further Development of the General Theory Chapter 9. The Kleene Hierarchy 1. The Interation Theorem 2. Some First Applications of the Iteration Theorem 3. Predicates, Sets, and Functions 4. Strong Reducibility 5. Some Classes of Predicates 6. A Representation Theorem for P subscript 2 superscript A 7. Post's Representation Theorem Chapter 10. Computable Functionals 1. Functionals 2. Complete Computable functionals 3. Normal Form Theorems 4. Partially Computable and Computable Functionals 5. Functionals and Relative Recursiveness 6. Decision Problems 7. The Recursion Theorems Chapter 11. The Classification of Unsolvable Decision Problems 1. Reducibility and the Kleene Hierarchy 2. Incomparability 3. Creative Sets and Simple Sets 4. Constructive Ordinals 5. Extensions of the Kleene Hierarchy Appendix 1. Some Results from the Elementary Theory of Numbers Appendix 2. Hilbert's Tenth Problem is Unsolvable References; Index

Edition DescriptionReprint,New Edition

SynopsisIn this classic text, Dr. Davis provides a clear introduction to computability, at an advanced undergraduate level, that serves the needs of specialists and non-specialists alike. In Part One (Chapters 1-5), Professor Davis outlines the general theory of computability, discussing such topics as computable functions, operations on computable functions, recursive functions, Turing machines, self-applied, and unsolvable decision problems. The author has been careful, especially in the first seven chapters, to assume no special mathematical training on the part of the reader. Part Two (Chapters 6-8) comprises a concise treatment of applications of the general theory, incorporating material on combinatorial problems, Diophantine Equations (including Hilbert's Tenth Problem) and mathematical logic. The final three chapters (Part 3) present further development of the general theory, encompassing the Kleene hierarchy, computable functionals, and the classification of unsolvable decision problems. When first published in 1958, this work introduced much terminology that has since become standard in theoretical computer science. Indeed, the stature of the book is such that many computer scientists regard it as their theoretical introduction to the topic. This new Dover edition makes this pioneering, widely admired text available in an inexpensive format. For Dover's edition, Dr. Davis has provided a new Preface and an Appendix, "Hilbert's Tenth Problem Is Unsolvable," an important article he published in The American Mathematical Monthly in 1973, which was awarded prizes by the American Mathematical Society and the Mathematical Association of America. These additions further enhance the value and usefulness of an "unusually clear and stimulating exposition" (Centre National de la Recherche Scientifique, Paris) now available for the first time in paperback., Classic text considers general theory of computability, computable functions, operations on computable functions, Turing machines self-applied, unsolvable decision problems, applications of general theory, mathematical logic, Kleene hierarchy, computable functionals, classification of unsolvable decision problems and more., Classic graduate-level introduction to theory of computability. Discusses general theory of computability, computable functions, operations on computable functions, Turing machines self-applied, unsolvable decision problems, applications of general theory, mathematical logic, Kleene hierarchy, more.

LC Classification NumberQA9.615.D3