Complexity In Information Theory
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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).
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.
Elements Of Information Theory
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Author : Thomas M. Cover
language : en
Publisher: John Wiley & Sons
Release Date : 2012-11-28
Elements Of Information Theory written by Thomas M. Cover and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-28 with Computers categories.
The latest edition of this classic is updated with new problem sets and material The Second Edition of this fundamental textbook maintains the book's tradition of clear, thought-provoking instruction. Readers are provided once again with an instructive mix of mathematics, physics, statistics, and information theory. All the essential topics in information theory are covered in detail, including entropy, data compression, channel capacity, rate distortion, network information theory, and hypothesis testing. The authors provide readers with a solid understanding of the underlying theory and applications. Problem sets and a telegraphic summary at the end of each chapter further assist readers. The historical notes that follow each chapter recap the main points. The Second Edition features: Chapters reorganized to improve teaching 200 new problems New material on source coding, portfolio theory, and feedback capacity Updated references Now current and enhanced, the Second Edition of Elements of Information Theory remains the ideal textbook for upper-level undergraduate and graduate courses in electrical engineering, statistics, and telecommunications.
Complexity And Information
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Author : J. F. Traub
language : en
Publisher: Cambridge University Press
Release Date : 1998-12-10
Complexity And Information written by J. F. Traub 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 1998-12-10 with Computers categories.
The twin themes of computational complexity and information pervade this 1998 book. It starts with an introduction to the computational complexity of continuous mathematical models, that is, information-based complexity. This is then used to illustrate a variety of topics, including breaking the curse of dimensionality, complexity of path integration, solvability of ill-posed problems, the value of information in computation, assigning values to mathematical hypotheses, and new, improved methods for mathematical finance. The style is informal, and the goals are exposition, insight and motivation. A comprehensive bibliography is provided, to which readers are referred for precise statements of results and their proofs. As the first introductory book on the subject it will be invaluable as a guide to the area for the many students and researchers whose disciplines, ranging from physics to finance, are influenced by the computational complexity of continuous problems.
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.
Information Spectrum Methods In Information Theory
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Author : Te Sun Han
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-18
Information Spectrum Methods In Information Theory written by Te Sun Han 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 2013-04-18 with Mathematics categories.
From the reviews: "This book nicely complements the existing literature on information and coding theory by concentrating on arbitrary nonstationary and/or nonergodic sources and channels with arbitrarily large alphabets. Even with such generality the authors have managed to successfully reach a highly unconventional but very fertile exposition rendering new insights into many problems." -- MATHEMATICAL REVIEWS
Information Theory In Computer Vision And Pattern Recognition
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Author : Francisco Escolano Ruiz
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-07-14
Information Theory In Computer Vision And Pattern Recognition written by Francisco Escolano Ruiz 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 2009-07-14 with Computers categories.
Information theory has proved to be effective for solving many computer vision and pattern recognition (CVPR) problems (such as image matching, clustering and segmentation, saliency detection, feature selection, optimal classifier design and many others). Nowadays, researchers are widely bringing information theory elements to the CVPR arena. Among these elements there are measures (entropy, mutual information...), principles (maximum entropy, minimax entropy...) and theories (rate distortion theory, method of types...). This book explores and introduces the latter elements through an incremental complexity approach at the same time where CVPR problems are formulated and the most representative algorithms are presented. Interesting connections between information theory principles when applied to different problems are highlighted, seeking a comprehensive research roadmap. The result is a novel tool both for CVPR and machine learning researchers, and contributes to a cross-fertilization of both areas.
Complexity Theory And Cryptology
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Author : Jörg Rothe
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-07-22
Complexity Theory And Cryptology written by Jörg Rothe 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 2005-07-22 with Computers categories.
Modern cryptology increasingly employs mathematically rigorous concepts and methods from complexity theory. Conversely, current research topics in complexity theory are often motivated by questions and problems from cryptology. This book takes account of this situation, and therefore its subject is what may be dubbed "cryptocomplexity'', a kind of symbiosis of these two areas. This book is written for undergraduate and graduate students of computer science, mathematics, and engineering, and can be used for courses on complexity theory and cryptology, preferably by stressing their interrelation. Moreover, it may serve as a valuable source for researchers, teachers, and practitioners working in these fields. Starting from scratch, it works its way to the frontiers of current research in these fields and provides a detailed overview of their history and their current research topics and challenges.
Complexity Theory
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Author : Ingo Wegener
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-04-11
Complexity Theory written by Ingo Wegener 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 2005-04-11 with Computers categories.
Reflects recent developments in its emphasis on randomized and approximation algorithms and communication models All topics are considered from an algorithmic point of view stressing the implications for algorithm design
Information Theory And Network Coding
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Author : Raymond W. Yeung
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-10
Information Theory And Network Coding written by Raymond W. Yeung 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 2008-09-10 with Computers categories.
This book is an evolution from my book A First Course in Information Theory published in 2002 when network coding was still at its infancy. The last few years have witnessed the rapid development of network coding into a research ?eld of its own in information science. With its root in infor- tion theory, network coding has not only brought about a paradigm shift in network communications at large, but also had signi?cant in?uence on such speci?c research ?elds as coding theory, networking, switching, wireless c- munications,distributeddatastorage,cryptography,andoptimizationtheory. While new applications of network coding keep emerging, the fundamental - sults that lay the foundation of the subject are more or less mature. One of the main goals of this book therefore is to present these results in a unifying and coherent manner. While the previous book focused only on information theory for discrete random variables, the current book contains two new chapters on information theory for continuous random variables, namely the chapter on di?erential entropy and the chapter on continuous-valued channels. With these topics included, the book becomes more comprehensive and is more suitable to be used as a textbook for a course in an electrical engineering department.