Computability

Computability : An Introduction to Recursive Function Theory

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Description

What can computers do in principle? What are their inherent theoretical limitations? These are questions to which computer scientists must address themselves. The theoretical framework which enables such questions to be answered has been developed over the last fifty years from the idea of a computable function: intuitively a function whose values can be calculated in an effective or automatic way. This book is an introduction to computability theory (or recursion theory as it is traditionally known to mathematicians). Dr Cutland begins with a mathematical characterisation of computable functions using a simple idealised computer (a register machine); after some comparison with other characterisations, he develops the mathematical theory, including a full discussion of non-computability and undecidability, and the theory of recursive and recursively enumerable sets. The later chapters provide an introduction to more advanced topics such as Gildel's incompleteness theorem, degrees of unsolvability, the Recursion theorems and the theory of complexity of computation. Computability is thus a branch of mathematics which is of relevance also to computer scientists and philosophers. Mathematics students with no prior knowledge of the subject and computer science students who wish to supplement their practical expertise with some theoretical background will find this book of use and interest.show more

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Review quote

"Dr. Cutland has produced here an excellent and much needed textbook which will undoubtedly help to establish recursion theory as a more widely taught branch of mainstream mathematics." Mathematics & Physicsshow more

Table of contents

Preface; Prologue, prerequisites and notation; 1. Computable functions; 2. Generating computable functions; 3. Other approaches to computability: Church's thesis; 4. Numbering computable functions; 5. Universal programs; 6. Decidability, undecidability and partical decidability; 7. Recursive and recursively enumerable sets; 8. Arithmetic and Godel's incompleteness theorem; 9. Reducibility and degrees; 10. Effective operations on partial functions; 11. The second recursion theorem; 12. Complexity of computation; 13. Further study.show more

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