Kolmogorov Complexity and Algorithmic Randomness

V. A. Uspensky, N. Vereshchagin, A. Shen

ISBN 10: 1470470640 / ISBN 13: 9781470470647

Published by American Mathematical Society, US, 2017

About this Item

Looking at a sequence of zeros and ones, we often feel that it is not random, that is, it is not plausible as an outcome of fair coin tossing. Why? The answer is provided by algorithmic information theory: because the sequence is compressible, that is, it has small complexity or, equivalently, can be produced by a short program. This idea, going back to Solomonoff, Kolmogorov, Chaitin, Levin, and others, is now the starting point of algorithmic information theory.The first part of this book is a textbook-style exposition of the basic notions of complexity and randomness; the second part covers some recent work done by participants of the "Kolmogorov seminar" in Moscow (started by Kolmogorov himself in the 1980s) and their colleagues.This book contains numerous exercises (embedded in the text) that will help readers to grasp the material.

Seller Inventory # LU-9781470470647

Bibliographic Details

• Title: Kolmogorov Complexity and Algorithmic Randomness
• Publisher: American Mathematical Society, US
• Publication Date: 2017
• Language: English
• ISBN 10: 1470470640
• ISBN 13: 9781470470647
• Binding: Paperback
• Condition: New

About this title

Synopsis

Looking at a sequence of zeros and ones, we often feel that it is not random, that is, it is not plausible as an outcome of fair coin tossing. Why? The answer is provided by algorithmic information theory: because the sequence is compressible, that is, it has small complexity or, equivalently, can be produced by a short program. This idea, going back to Solomonoff, Kolmogorov, Chaitin, Levin, and others, is now the starting point of algorithmic information theory. The first part of this book is a textbook-style exposition of the basic notions of complexity and randomness; the second part covers some recent work done by participants of the “Kolmogorov seminar” in Moscow (started by Kolmogorov himself in the 1980s) and their colleagues. This book contains numerous exercises (embedded in the text) that will help readers to grasp the material.

About the Author

A. Shen, LIRMM CRNS, Université de Montpellier, France, V. A. Uspensky, Lomonosov Moscow State University, Russia, and N. Vereshchagin, Lomonosov Moscow State University, Russia