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
10 December 2008

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.

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.

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: 239mm, Width: 162mm, Spine: 27mm
Weight: 1g
ISBN: 9780199230761
ISBN 10: 0199230765
Series: Oxford Logic Guides
Pages: 450
Publication Date: 10 December 2008
Audience: College/higher education , Professional and scholarly , Further / Higher Education , Undergraduate
Format: Hardback
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

André Nies received his PhD in Mathematics form the University of Heidelberg, Germany, in 1992. From 1994 to 1995 he was a Visiting Professor at the University of Wisconsin at Madison and Cornell. In 1995 he took the post of Assistant Professor at the University of Chicago. Since 2002 he has been Senior Lecturer in the Department of Computer Science, University of Aukland.

Reviews for Computability and Randomness

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