Kolmogorov complexity and algorithmic randomness
著者
書誌事項
Kolmogorov complexity and algorithmic randomness
（Mathematical surveys and monographs, v. 220）
American Mathematical Society, c2017
- タイトル別名
-
Колмогоровская сложность и алгоритмическая случайность
大学図書館所蔵 件 / 全31件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
Includes bibliographical references (p. 491-500) and indexes
内容説明・目次
内容説明
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.
目次
Plain Kolmogorov complexity
Complexity of pairs and conditional complexity
Martin-Lof randomness
A priori probability and prefix complexity
Monotone complexity
General scheme for complexities
Shannon entropy and Kolmogorov complexity
Some applications
Frequency and game approaches to randomness
Inequalities for entropy, complexity, and size
Common information
Multisource algorithmic information theory
Information and logic
Algorithmic statistics
Complexity and foundations of probability
Four algorithmic faces of randomness
Bibliography
Name index
Subject Index.
「Nielsen BookData」 より