Kolmogorov Complexity And Algorithmic Randomness
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Algorithmic Randomness And Complexity
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Author : Rodney G. Downey
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-29
Algorithmic Randomness And Complexity written by Rodney G. Downey and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-29 with Computers categories.
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
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Author : A. Shen
language : en
Publisher: American Mathematical Society
Release Date : 2022-05-18
Kolmogorov Complexity And Algorithmic Randomness written by A. Shen and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-18 with Mathematics categories.
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.
An Introduction To Kolmogorov Complexity And Its Applications
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Author : Ming Li
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
An Introduction To Kolmogorov Complexity And Its Applications written by Ming Li and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
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).
Kolmogorov Complexity And Algorithmic Randomness
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Author : A. Shen
language : en
Publisher:
Release Date : 2017
Kolmogorov Complexity And Algorithmic Randomness written by A. Shen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with MATHEMATICS categories.
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 cover.
Kolmogorov Complexity And Algorithmic Randomness
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Author : Alexander Shen
language : en
Publisher:
Release Date : 2017
Kolmogorov Complexity And Algorithmic Randomness written by Alexander Shen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Computational complexity categories.
Kolmogorov Complexity And Algorithmic Randomness
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Author : Amy Katherine Lorentz
language : en
Publisher:
Release Date : 1994
Kolmogorov Complexity And Algorithmic Randomness written by Amy Katherine Lorentz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with categories.
Information And Randomness
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Author : Cristian Calude
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Information And Randomness written by Cristian Calude and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Computers categories.
"Algorithmic information theory (AIT) is the result of putting Shannon's information theory and Turing's computability theory into a cocktail shaker and shaking vigorously", says G.J. Chaitin, one of the fathers of this theory of complexity and randomness, which is also known as Kolmogorov complexity. It is relevant for logic (new light is shed on Gödel's incompleteness results), physics (chaotic motion), biology (how likely is life to appear and evolve?), and metaphysics (how ordered is the universe?). This book, benefiting from the author's research and teaching experience in Algorithmic Information Theory (AIT), should help to make the detailed mathematical techniques of AIT accessible to a much wider audience.
An Introduction To Kolmogorov Complexity And Its Applications
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Author : Ming Li
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-02-27
An Introduction To Kolmogorov Complexity And Its Applications written by Ming Li and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-02-27 with Mathematics categories.
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).
Computational Complexity
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Author : Sanjeev Arora
language : en
Publisher: Cambridge University Press
Release Date : 2009-04-20
Computational Complexity written by Sanjeev Arora and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-20 with Computers categories.
New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.
Algorithmic Learning In A Random World
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Author : Vladimir Vovk
language : en
Publisher: Springer
Release Date : 2010-10-29
Algorithmic Learning In A Random World written by Vladimir Vovk and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-29 with Computers categories.
Algorithmic Learning in a Random World describes recent theoretical and experimental developments in building computable approximations to Kolmogorov's algorithmic notion of randomness. Based on these approximations, a new set of machine learning algorithms have been developed that can be used to make predictions and to estimate their confidence and credibility in high-dimensional spaces under the usual assumption that the data are independent and identically distributed (assumption of randomness). Another aim of this unique monograph is to outline some limits of predictions: The approach based on algorithmic theory of randomness allows for the proof of impossibility of prediction in certain situations. The book describes how several important machine learning problems, such as density estimation in high-dimensional spaces, cannot be solved if the only assumption is randomness.