Computability theory
著者
書誌事項
Computability theory
（Student mathematical library, v. 62）
American Mathematical Society, c2012
- : pbk
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注記
Includes bibliographical references (p. 193-197) and index
内容説明・目次
内容説明
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.
目次
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
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