Computability Nigel Cutland 1139929879 9781139929875

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Product details:

• ISBN 10: 1139929879
• ISBN 13: 9781139929875
• Author: Nigel Cutland

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 Gödel’s incompleteness theorem, degrees of unsolvability, the Recursion theorems and the theory of complexity of computation.

Table of contents:

1  Algorithms, or effective procedures

2  The unlimited register machine

3  URM-computable functions

4  Decidable predicates and problems

5  Computability on other domains

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