Computability: An Introduction to Recursive Function Theory

by 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 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. 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.

Genres: Computer Science, Mathematics, Nonfiction, Programming

264 pages, Paperback

First published January 1, 1980

Reviews

[Emilia Dunfelt · Rating 4 out of 5]

Good read, a great introduction to the topic. Nice selection of exercises and examples.

[Ivan · Rating 3 out of 5]

This is not an easy book. Most of the concepts it talks about are quite complex, and you'll need some advanced math knowledge to really understand what it's talking about. That said, if you want to get started in computability theory this book is a really nice introductory text.

Keep in mind, though, that this is a quite old book so since it has been published a lot of new proofs have been discovered. Because of this it also don't talk in depth about the complexity classes like P, NP, EXP and so on and focuses a lot on unlimited registers machines rather than Turing machines. Anyway, before you get seriously started on any of these topics you really need the basics this book can give you.