Complexity In Information Theory
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Complexity In Information Theory
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Author : Yaser S. Abu-Mostafa
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Complexity In Information Theory written by Yaser S. Abu-Mostafa 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 means and ends of information theory and computational complexity have grown significantly closer over the past decade. Common analytic tools, such as combinatorial mathematics and information flow arguments, have been the cornerstone of VLSl complexity and cooperative computation. The basic assumption of limited computing resources is the premise for cryptography, where the distinction is made between available information and accessible information. Numerous other examples of common goals and tools between the two disciplines have shaped a new research category of 'information and complexity theory'. This volume is intended to expose to the research community some of the recent significant topics along this theme. The contributions selected here are all very basic, presently active, fairly well-established, and stimulating for substantial follow-ups. This is not an encyclopedia on the subject, it is concerned only with timely contributions of sufficient coherence and promise. The styles of the six chapters cover a wide spectrum from specific mathematical results to surveys of large areas. It is hoped that the technical content and theme of this volume will help establish this general research area. I would like to thank the authors of the chapters for contributing to this volume. I also would like to thank Ed Posner for his initiative to address this subject systematically, and Andy Fyfe and Ruth Erlanson for proofreading some of the chapters.
Information And Complexity
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Author : Mark Burgin
language : en
Publisher: World Scientific
Release Date : 2016-11-28
Information And Complexity written by Mark Burgin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-28 with Computers categories.
The book is a collection of papers of experts in the fields of information and complexity. Information is a basic structure of the world, while complexity is a fundamental property of systems and processes. There are intrinsic relations between information and complexity.The research in information theory, the theory of complexity and their interrelations is very active. The book will expand knowledge on information, complexity and their relations representing the most recent and advanced studies and achievements in this area.The goal of the book is to present the topic from different perspectives — mathematical, informational, philosophical, methodological, etc.
Entropy Search Complexity
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Author : Imre Csiszár
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-04-05
Entropy Search Complexity written by Imre Csiszár 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 2007-04-05 with Mathematics categories.
This book collects survey papers in the fields of entropy, search and complexity, summarizing the latest developments in their respective areas. More than half of the papers belong to search theory which lies on the borderline of mathematics and computer science, information theory and combinatorics, respectively. The book will be useful to experienced researchers as well as young scientists and students both in mathematics and computer science.
An Introduction To Kolmogorov Complexity And Its Applications
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Author : Ming Li
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-03-18
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 2009-03-18 with Mathematics categories.
“The book is outstanding and admirable in many respects. ... is necessary reading for all kinds of readers from undergraduate students to top authorities in the field.” Journal of Symbolic Logic Written by two experts in the field, this is the only comprehensive and unified treatment of the central ideas and applications of Kolmogorov complexity. The book presents a thorough treatment of the subject with a wide range of illustrative applications. Such applications include the randomness of finite objects or infinite sequences, Martin-Loef tests for randomness, information theory, computational learning theory, the complexity of algorithms, and the thermodynamics of computing. It will be ideal for advanced undergraduate students, graduate students, and researchers in computer science, mathematics, cognitive sciences, philosophy, artificial intelligence, statistics, and physics. The book is self-contained in that it contains the basic requirements from mathematics and computer science. Included are also numerous problem sets, comments, source references, and hints to solutions of problems. New topics in this edition include Omega numbers, Kolmogorov–Loveland randomness, universal learning, communication complexity, Kolmogorov's random graphs, time-limited universal distribution, Shannon information and others.
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.
Complexity Entropy And The Physics Of Information
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Author : Wojciech H. Zurek
language : en
Publisher: CRC Press
Release Date : 2018-03-08
Complexity Entropy And The Physics Of Information written by Wojciech H. Zurek and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-08 with Science categories.
This book has emerged from a meeting held during the week of May 29 to June 2, 1989, at St. John’s College in Santa Fe under the auspices of the Santa Fe Institute. The (approximately 40) official participants as well as equally numerous “groupies” were enticed to Santa Fe by the above “manifesto.” The book—like the “Complexity, Entropy and the Physics of Information” meeting explores not only the connections between quantum and classical physics, information and its transfer, computation, and their significance for the formulation of physical theories, but it also considers the origins and evolution of the information-processing entities, their complexity, and the manner in which they analyze their perceptions to form models of the Universe. As a result, the contributions can be divided into distinct sections only with some difficulty. Indeed, I regard this degree of overlapping as a measure of the success of the meeting. It signifies consensus about the important questions and on the anticipated answers: they presumably lie somewhere in the “border territory,” where information, physics, complexity, quantum, and computation all meet.
Complexity In Information Theory
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Author : Yaser S Abu-Mostafa
language : en
Publisher:
Release Date : 1988-11-01
Complexity In Information Theory written by Yaser S Abu-Mostafa and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-11-01 with categories.
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.
Information And Complexity In Statistical Modeling
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Author : Jorma Rissanen
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-15
Information And Complexity In Statistical Modeling written by Jorma Rissanen 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 2007-12-15 with Mathematics categories.
No statistical model is "true" or "false," "right" or "wrong"; the models just have varying performance, which can be assessed. The main theme in this book is to teach modeling based on the principle that the objective is to extract the information from data that can be learned with suggested classes of probability models. The intuitive and fundamental concepts of complexity, learnable information, and noise are formalized, which provides a firm information theoretic foundation for statistical modeling. Although the prerequisites include only basic probability calculus and statistics, a moderate level of mathematical proficiency would be beneficial.
Algorithmic Complexity And Telecommunication Problems
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Author : J-P Barthelmy
language : en
Publisher: CRC Press
Release Date : 2020-08-13
Algorithmic Complexity And Telecommunication Problems written by J-P Barthelmy and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-13 with Computers categories.
In this treatment of algorithmic complexity the authors explore an area fundamental to the study of the foundations of computer science. It is a topic which is at the interface of information theory, applied mathematics and computer language theory and which is rooted strongly in this book in the problems of computer communication.; Complexity theory classifies problems according to the difficulty of resolving them, while algorithms provide the computational method for solving those problems. Therefore, algorithmic complexity is concerned with establishing the best algorithm given the constraints of the computational environment and the degree of complexity.; The first three chapters present the context for a later in-depth look at applied areas of the subject, with an outline of classical complexity theory. This is followed by three chapters which explore the key area of information communication. Within this field, the book is particularly concerned with two contiguous areas which make contrasting demands on the application of algorithmic complexity. Cryptography demands the creation of extremely complex problems in order to achieve its goal of security, whereas in coding for communication the emphasis is on maximizing the compact nature of the message and providing the error correction necessary for the message to achieve optimum speed. The two must co-exist and the methods outlined in "Algorithmic Complexity" suggest a number of approaches to such problems based on extensive examples of the authors' experience.; This senior undergraduate book should be an essential read for those studying advanced topics in theoretical computer science and should provide an introduction to applied complexity for researchers and professionals alike.