Computability theory
Author(s)
Bibliographic Information
Computability theory
（Student mathematical library, v. 62）
American Mathematical Society, c2012
- : pbk
Available at 31 libraries
-
Library, Research Institute for Mathematical Sciences, Kyoto University数研
: pbkWEB||11||1200026122190
Note
Includes bibliographical references (p. 193-197) and index
Description and Table of Contents
Description
What can we compute--even with unlimited resources? Is everything within reach? Or are computations necessarily drastically limited, not just in practice, but theoretically? These questions are at the heart of computability theory. The goal of this book is to give the reader a firm grounding in the fundamentals of computability theory and an overview of currently active areas of research, such as reverse mathematics and algorithmic randomness. Turing machines and partial recursive functions are explored in detail, and vital tools and concepts including coding, uniformity, and diagonalization are described explicitly. From there the material continues with universal machines, the halting problem, parametrization and the recursion theorem, and thence to computability for sets, enumerability, and Turing reduction and degrees. A few more advanced topics round out the book before the chapter on areas of research. The text is designed to be self-contained, with an entire chapter of preliminary material including relations, recursion, induction, and logical and set notation and operators. That background, along with ample explanation, examples, exercises, and suggestions for further reading, make this book ideal for independent study or courses with few prerequisites.
Table of Contents
Introduction
Background
Defining computability
Working with computable functions
Computing and enumerating sets
Turing reduction and Post’s problem
Two hierarchies of sets
Further tools and results
Areas of research
Mathematical asides
Bibliography
Index
by "Nielsen BookData"