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An Introduction to Kolmogorov Complexity and Its Applications

2013-03-09 Mathematics
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Release : 2013-03-09
Genre : Mathematics
Kind : eBook
Book Rating : 066/5 ( reviews)

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Book Synopsis An Introduction to Kolmogorov Complexity and Its Applications by : Ming Li

Download or read book An Introduction to Kolmogorov Complexity and Its Applications written by Ming Li. This book was released on 2013-03-09. Available in PDF, EPUB and Kindle. Book excerpt: Briefly, we review the basic elements of computability theory and prob ability theory that are required. Finally, in order to place the subject in the appropriate historical and conceptual context we trace the main roots of Kolmogorov complexity. This way the stage is set for Chapters 2 and 3, where we introduce the notion of optimal effective descriptions of objects. The length of such a description (or the number of bits of information in it) is its Kolmogorov complexity. We treat all aspects of the elementary mathematical theory of Kolmogorov complexity. This body of knowledge may be called algo rithmic complexity theory. The theory of Martin-Lof tests for random ness of finite objects and infinite sequences is inextricably intertwined with the theory of Kolmogorov complexity and is completely treated. We also investigate the statistical properties of finite strings with high Kolmogorov complexity. Both of these topics are eminently useful in the applications part of the book. We also investigate the recursion theoretic properties of Kolmogorov complexity (relations with Godel's incompleteness result), and the Kolmogorov complexity version of infor mation theory, which we may call "algorithmic information theory" or "absolute information theory. " The treatment of algorithmic probability theory in Chapter 4 presup poses Sections 1. 6, 1. 11. 2, and Chapter 3 (at least Sections 3. 1 through 3. 4).

An Introduction to Kolmogorov Complexity and Its Applications

1997-02-27 Mathematics
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Release : 1997-02-27
Genre : Mathematics
Kind : eBook
Book Rating : 683/5 ( reviews)

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Book Synopsis An Introduction to Kolmogorov Complexity and Its Applications by : Ming Li

Download or read book An Introduction to Kolmogorov Complexity and Its Applications written by Ming Li. This book was released on 1997-02-27. Available in PDF, EPUB and Kindle. Book excerpt: Briefly, we review the basic elements of computability theory and prob ability theory that are required. Finally, in order to place the subject in the appropriate historical and conceptual context we trace the main roots of Kolmogorov complexity. This way the stage is set for Chapters 2 and 3, where we introduce the notion of optimal effective descriptions of objects. The length of such a description (or the number of bits of information in it) is its Kolmogorov complexity. We treat all aspects of the elementary mathematical theory of Kolmogorov complexity. This body of knowledge may be called algo rithmic complexity theory. The theory of Martin-Lof tests for random ness of finite objects and infinite sequences is inextricably intertwined with the theory of Kolmogorov complexity and is completely treated. We also investigate the statistical properties of finite strings with high Kolmogorov complexity. Both of these topics are eminently useful in the applications part of the book. We also investigate the recursion theoretic properties of Kolmogorov complexity (relations with Godel's incompleteness result), and the Kolmogorov complexity version of infor mation theory, which we may call "algorithmic information theory" or "absolute information theory. " The treatment of algorithmic probability theory in Chapter 4 presup poses Sections 1. 6, 1. 11. 2, and Chapter 3 (at least Sections 3. 1 through 3. 4).

An Introduction to Kolmogorov Complexity and Its Applications

2013-04-18 Computers
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Release : 2013-04-18
Genre : Computers
Kind : eBook
Book Rating : 609/5 ( reviews)

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Book Synopsis An Introduction to Kolmogorov Complexity and Its Applications by : Ming Li

Download or read book An Introduction to Kolmogorov Complexity and Its Applications written by Ming Li. This book was released on 2013-04-18. Available in PDF, EPUB and Kindle. Book excerpt: With this book, the authors are trying to present in a unified treatment an introduction to the central ideas and their applications of the Kolmogorov Complexity, the theory dealing with the quantity of information in individual objects. This book is appropriate for either a one- or two-semester introductory course in departments of computer science, mathematics, physics, probability theory and statistics, artificial intelligence, and philosophy. Although the mathematical theory of Kolmogorov complexity contains sophisticated mathematics, the amount of math one needs to know to apply the notions in widely divergent areas, is very little. The authors' purpose is to develop the theory in detail and outline a wide range of illustrative applications. This book is an attempt to grasp the mass of fragmented knowledge of this fascinating theory. Chapter 1 is a compilation of material on the diverse notations and disciplines we draw upon in order to make the book self-contained. The mathematical theory of Kolmogorov complexity is treated in chapters 2-4; the applications are treated in chapters 4-8.

Algorithmic Randomness and Complexity

2010-10-29 Computers
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Release : 2010-10-29
Genre : Computers
Kind : eBook
Book Rating : 417/5 ( reviews)

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Book Synopsis Algorithmic Randomness and Complexity by : Rodney G. Downey

Download or read book Algorithmic Randomness and Complexity written by Rodney G. Downey. This book was released on 2010-10-29. Available in PDF, EPUB and Kindle. Book excerpt: Computability and complexity theory are two central areas of research in theoretical computer science. This book provides a systematic, technical development of "algorithmic randomness" and complexity for scientists from diverse fields.

Kolmogorov Complexity and Algorithmic Randomness

2017-11-02 Computers
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Release : 2017-11-02
Genre : Computers
Kind : eBook
Book Rating : 823/5 ( reviews)

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Book Synopsis Kolmogorov Complexity and Algorithmic Randomness by : A. Shen

Download or read book Kolmogorov Complexity and Algorithmic Randomness written by A. Shen. This book was released on 2017-11-02. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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