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. Computability is thus a branch of mathematics which is of relevance also to computer scientists and philosophers.

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About this title 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.

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.

Book Description: This introduction to recursive theory computability begins with a mathematical characterization of computable functions, develops the mathematical theory and includes a full discussion of noncomputability and undecidability. Review: "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.

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## Computability, an introduction to recursive function theory

Many-one reducibility This is essentially one-one reducibility without the constraint that f be injective. A is many-one reducible or m-reducible to B if there is a total computable function f such that each n is in A if and only if f n is in B. Truth-table reducibility A is truth-table reducible to B if A is Turing reducible to B via an oracle Turing machine that computes a total function regardless of the oracle it is given. Many variants of truth-table reducibility have also been studied.

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## Computability theory

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## ISBN 13: 9780521294652

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