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Computability and Randomness (Oxford Logic Guides) 🔍
André Nies Oxford University Press, USA, Oxford Logic Guides 51, 2009
英语 [en] · PDF · 2.8MB · 2009 · 📘 非小说类图书 · 🚀/lgli/lgrs · Save
描述
The interplay between computability and randomness has been an active area of research in recent years, reflected by ample funding in the USA, numerous workshops, and publications on the subject. The complexity and the randomness aspect of a set of natural numbers are closely related. Traditionally, computability theory is concerned with the complexity aspect. However, computability theoretic tools can also be used to introduce mathematical counterparts for the intuitive notion of randomness of a set. Recent research shows that, conversely, concepts and methods originating from randomness enrich computability theory. The book covers topics such as lowness and highness properties, Kolmogorov complexity, betting strategies and higher computability. Both the basics and recent research results are desribed, providing a very readable introduction to the exciting interface of computability and randomness for graduates and researchers in computability theory, theoretical computer science, and measure theory.
备用文件名
lgrsnf/_426259.214416d4fa45c33a27eb6d39dc0ba212.pdf
备选作者
Nies, André
备选作者
Andre Nies
备用出版商
IRL Press at Oxford University Press
备用出版商
Oxford Institute for Energy Studies
备用出版商
German Historical Institute London
备用出版商
OUP Oxford
备用版本
United Kingdom and Ireland, United Kingdom
备用版本
Oxford University Press USA, Oxford, 2009
备用版本
Oxford logic guides, Oxford, 2008
备用版本
Oxford logic guides, Oxford, 2009
备用版本
New York, New York State, 2009
备用版本
1, FR, 2009
元数据中的注释
до 2011-08
元数据中的注释
lg693046
备用描述
The interplay between computability and randomness has been an active area of research in recent years, reflected by ample funding in the USA, numerous workshops, and publications on the subject. The complexity and the randomness aspect of a set of natural numbers are closely related. Traditionally, computability theory is concerned with the complexity aspect. However, computability theoretic tools can also be used to introduce mathematical counterparts for the intuitive notion of randomness of a set. Recent research shows that, conversely, concepts and methods originating from randomness enrich computability theory.
Covering the basics as well as recent research results, this book provides a very readable introduction to the exciting interface of computability and randomness for graduates and researchers in computability theory, theoretical computer science, and measure theory.
备用描述
A Monograph On The Computational Complexity And Randomness Of Sets Of Natural Numbers. Preface; 1. The Complexity Of Sets; 2. The Descriptive Complexity Of Strings; 3. Martin-lof Randomness And Its Variants; 4. Diagonally Noncomputable Functions; 5. Lowness Properties And K-triviality; 6. Some Advanced Computability Theory; 7. Randomness And Betting Strategies; 8. Classes Of Computational Complexity; 9. Higher Computability And Randomness; Solutions To Exercises; References; Index. André Nies. Includes Bibliographical References (p. [410]-417) And Indexes.
开源日期
2011-08-31
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