On The Use Of Kolmogorov Complexity In Computational Complexity
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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 Computational Complexity
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Author : Osamu Watanabe
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Kolmogorov Complexity And Computational Complexity written by Osamu Watanabe 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 2012-12-06 with Computers categories.
The mathematical theory of computation has given rise to two important ap proaches to the informal notion of "complexity": Kolmogorov complexity, usu ally a complexity measure for a single object such as a string, a sequence etc., measures the amount of information necessary to describe the object. Compu tational complexity, usually a complexity measure for a set of objects, measures the compuational resources necessary to recognize or produce elements of the set. The relation between these two complexity measures has been considered for more than two decades, and may interesting and deep observations have been obtained. In March 1990, the Symposium on Theory and Application of Minimal Length Encoding was held at Stanford University as a part of the AAAI 1990 Spring Symposium Series. Some sessions of the symposium were dedicated to Kolmogorov complexity and its relations to the computational complexity the ory, and excellent expository talks were given there. Feeling that, due to the importance of the material, some way should be found to share these talks with researchers in the computer science community, I asked the speakers of those sessions to write survey papers based on their talks in the symposium. In response, five speakers from the sessions contributed the papers which appear in this book.
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.
On The Use Of Kolmogorov Complexity In Computational Complexity
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Author :
language : en
Publisher:
Release Date : 2001
On The Use Of Kolmogorov Complexity In Computational Complexity written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with categories.
The Minimum Description Length Principle
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Author : Peter D. Grünwald
language : en
Publisher: MIT Press
Release Date : 2007
The Minimum Description Length Principle written by Peter D. Grünwald and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Minimum description length (Information theory). categories.
This introduction to the MDL Principle provides a reference accessible to graduate students and researchers in statistics, pattern classification, machine learning, and data mining, to philosophers interested in the foundations of statistics, and to researchers in other applied sciences that involve model selection.
Introduction To The Theory Of Complexity
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Author : Daniel Pierre Bovet
language : en
Publisher: Prentice Hall PTR
Release Date : 1994
Introduction To The Theory Of Complexity written by Daniel Pierre Bovet and has been published by Prentice Hall PTR this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Computers categories.
Using a balanced approach that is partly algorithmic and partly structuralist, this book systematically reviews the most significant results obtained in the study of computational complexity theory. Features over 120 worked examples, over 200 problems, and 400 figures.
Universal Artificial Intelligence
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Author : Marcus Hutter
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-29
Universal Artificial Intelligence written by Marcus Hutter 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 2005-12-29 with Computers categories.
Personal motivation. The dream of creating artificial devices that reach or outperform human inteUigence is an old one. It is also one of the dreams of my youth, which have never left me. What makes this challenge so interesting? A solution would have enormous implications on our society, and there are reasons to believe that the AI problem can be solved in my expected lifetime. So, it's worth sticking to it for a lifetime, even if it takes 30 years or so to reap the benefits. The AI problem. The science of artificial intelligence (AI) may be defined as the construction of intelligent systems and their analysis. A natural definition of a system is anything that has an input and an output stream. Intelligence is more complicated. It can have many faces like creativity, solving prob lems, pattern recognition, classification, learning, induction, deduction, build ing analogies, optimization, surviving in an environment, language processing, and knowledge. A formal definition incorporating every aspect of intelligence, however, seems difficult. Most, if not all known facets of intelligence can be formulated as goal driven or, more precisely, as maximizing some utility func tion. It is, therefore, sufficient to study goal-driven AI; e. g. the (biological) goal of animals and humans is to survive and spread. The goal of AI systems should be to be useful to humans.
Kolmogorov Complexity And Computational Complexity
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Author : Osamu Watanabe
language : en
Publisher:
Release Date : 1992-10-26
Kolmogorov Complexity And Computational Complexity written by Osamu Watanabe and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-10-26 with categories.
There are many ways to measure the complexity of a given object, but there are two measures of particular importance in the theory of computing: One is Kolmogorov complexity, which measures the amount of information necessary to describe an object. Another is computational complexity, which measures the computational resources necessary to recognize (or produce) an object. The relation between these two complexity measures has been studied since the 1960s. More recently, the more generalized notion of resource bounded Kolmogorov complexity and its relation to computational complexity have received much attention. Now many interesting and deep observations on this topic have been established. This book consists of four survey papers concerning these recent studies on resource bounded Kolmogorov complexity and computational complexity. It also contains one paper surveying several types of Kolmogorov complexity measures. The papers are based on invited talks given at the AAAI Spring Symposium on Minimal-Length Encoding in 1990. The book is the only collection of survey papers on this subject and provides fundamental information for researchers in the field.
Advances In Minimum Description Length
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Author : Peter D. Grünwald
language : en
Publisher: MIT Press
Release Date : 2005
Advances In Minimum Description Length written by Peter D. Grünwald and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Computers categories.
A source book for state-of-the-art MDL, including an extensive tutorial and recent theoretical advances and practical applications in fields ranging from bioinformatics to psychology.