Computability and Randomness

The book covers topics such as lowness and highness properties, Kolmogorov complexity, betting strategies and higher computability.

Computability and Randomness

Computability and Randomness

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.

More Books:

Computability and Randomness
Language: en
Pages: 456
Authors: André Nies
Categories: Philosophy
Type: BOOK - Published: 2012-03-29 - Publisher: OUP Oxford

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
Randomness, Computability, and Algebraic Specifications
Language: en
Pages:
Authors: Bakhadyr Khoussainov
Categories: Philosophy
Type: BOOK - Published: 1996 - Publisher:

Books about Randomness, Computability, and Algebraic Specifications
Models of Computation in Context
Language: en
Pages: 319
Authors: Benedikt Löwe, Dag Normann, Ivan Soskov, Alexandra Soskova
Categories: Computers
Type: BOOK - Published: 2011-09-15 - Publisher: Springer

This book constitutes the refereed proceedings of the 7th Conference on Computability in Europe, CiE 2011, held in Sofia, Bulgaria, in June/July 2011. The 22 revised papers presented together with 11 invited lectures were carefully reviewed and selected with an acceptance rate of under 40%. The papers cover the topics
Algorithmic Randomness
Language: en
Pages: 300
Authors: Johanna N. Y. Franklin, Christopher P. Porter
Categories: Computers
Type: BOOK - Published: 2020-05-31 - Publisher: Cambridge University Press

Surveys on recent developments in the theory of algorithmic randomness and its interactions with other areas of mathematics.
Computability Theory and Its Applications
Language: en
Pages: 320
Authors: Peter Cholak, Steffen Lempp, Manuel Lerman, Richard A. Shore
Categories: Mathematics
Type: BOOK - Published: 2000 - Publisher: American Mathematical Soc.

This collection of articles presents a snapshot of the status of computability theory at the end of the millennium and a list of fruitful directions for future research. The papers represent the works of experts in the field who were invited speakers at the AMS-IMS-SIAM Joint Summer Conference on Computability

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