Computability and Randomness

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André Nies (, Senior Lecturer, Department of Computer Science, The University of Aukland)

Computability and Randomness

André Nies (, Senior Lecturer, Department of Computer Science, The University of Aukland)

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English

Oxford University Press
19 January 2012

Mathematics & Sciences; Philosophy of mathematics; Mathematical logic; Maths for computer scientists; Computer architecture & logic design

Series: Oxford Logic Guides

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.

By: André Nies ( Senior Lecturer Department of Computer Science The University of Aukland)
Imprint: Oxford University Press
Country of Publication: United Kingdom
Volume: 51
Dimensions: Height: 234mm, Width: 155mm, Spine: 25mm
Weight: 1g
ISBN: 9780199652600
ISBN 10: 0199652600
Series: Oxford Logic Guides
Pages: 456
Publication Date: 19 January 2012
Audience: College/higher education , Professional and scholarly , Further / Higher Education , Undergraduate
Format: Paperback
Publisher's Status: Active

Preface 1: The complexity of sets 2: The descriptive complexity of strings 3: Martin-Löf 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

Reviews for Computability and Randomness

Review from previous edition A great introduction to the field. It is well written and moves systematically to advanced topics. It can be used both as a reference and as a text book for a one-semester course in advanced algorithmic randomness and computability theory. Computing Reviews