Computability Theory pdf epub mobi txt 電子書下載2025

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出版者:American Mathematical Society

作者:Rebecca Weber

出品人:

頁數:203

译者:

出版時間:2012-5

價格:0

裝幀:Paperback

isbn號碼:9780821873922

叢書系列:Student Mathematical Library

圖書標籤:

MathLogic
Math
計算理論
可計算性
圖靈機
遞歸論
形式語言
算法
復雜性理論
邏輯學
數學基礎
理論計算機科學

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具體描述

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.

著者簡介

Rebecca Weber: Dartmouth College, Hanover, NH

圖書目錄

Cover 1
Title page 4
Contents 6
Introduction 10
Background 18
Defining computability 50
Working with computable functions 86
Computing and enumerating sets 104
Turing reduction and Post’s problem 118
Two hierarchies of sets 136
Further tools and results 148
Areas of research 158
Mathematical asides 198
Bibliography 202
Index 208
Back Cover 218
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