Paperback. 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 theintuitive notion of randomness of a set. Recent research shows that, conversely, concepts and methods originating from randomness enrich computability theory.The book covers topicssuch 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. A monograph on the interface of computational complexity and randomness of sets of natural numbers. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

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Bibliographic Details

Title: Computability and Randomness (Paperback)
Publisher: Oxford University Press, Oxford
Publication Date: 2012
Language: English
ISBN 10: 0199652600
ISBN 13: 9780199652600
Binding: Paperback
Condition: new

About this title

Synopsis

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.

About the Author

PhD, Mathematics, Univ. of Heidelberg, Germany, 1992
Univ of Wisconsin, Madison 1994
Cornell University 1995
Univ of Chicago 1995-2001
Habilitation, Univ. of Heidelberg, 1998
Univ of Auckland 2002-present.
60 journal and conference publications.
Invited Speaker, International Congress of Mathematicians, Hyderabad 2010

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