Download or read book An Introduction to Kolmogorov Complexity and Its Applications written by Ming Li and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 655 pages. 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).

Download or read book Lecture Notes on Descriptional Complexity and Randomness written by Peter Gacs and published by . This book was released on 2014-11-11 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lecture notes on descriptional complexity and randomnessBy Peter Gacs

Download or read book Algorithmic Randomness written by Johanna N. Y. Franklin and published by Cambridge University Press. This book was released on 2020-05-07 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last two decades have seen a wave of exciting new developments in the theory of algorithmic randomness and its applications to other areas of mathematics. This volume surveys much of the recent work that has not been included in published volumes until now. It contains a range of articles on algorithmic randomness and its interactions with closely related topics such as computability theory and computational complexity, as well as wider applications in areas of mathematics including analysis, probability, and ergodic theory. In addition to being an indispensable reference for researchers in algorithmic randomness, the unified view of the theory presented here makes this an excellent entry point for graduate students and other newcomers to the field.

Download or read book Kolmogorov Complexity and Algorithmic Randomness written by A. Shen and published by American Mathematical Soc.. This book was released on 2017-11-02 with total page 534 pages. 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.

Download or read book Algorithmic Randomness and Complexity written by Rodney G. Downey and published by Springer Science & Business Media. This book was released on 2010-10-29 with total page 883 pages. 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.

Download or read book Dynamics Information and Complexity in Quantum Systems written by Fabio Benatti and published by Springer Nature. This book was released on 2023-09-23 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition of Dynamics, Information and Complexity in Quantum Systems widens its scope by focussing more on the dynamics of quantum correlations and information in microscopic and mesoscopic systems, and their use for metrological and machine learning purposes. The book is divided into three parts: Part One: Classical Dynamical Systems Addresses classical dynamical systems, classical dynamical entropy, and classical algorithmic complexity. Includes a survey of the theory of simple perceptrons and their storage capacity. Part Two: Quantum Dynamical Systems Focuses on the dynamics of entanglement under dissipative dynamics and its metrological use in finite level quantum systems. Discusses the quantum fluctuation approach to large-scale mesoscopic systems and their emergent dynamics in quantum systems with infinitely many degrees of freedom. Introduces a model of quantum perceptron whose storage capacity is computed and compared with the classical one. Part Three: Quantum Dynamical Entropies and Complexities Devoted to quantum dynamical entropies and algorithmic complexities. This book is meant for advanced students, young and senior researchers working in the fields of quantum statistical mechanics, quantum information, and quantum dynamical systems. It is self-contained, and the only prerequisites needed are a standard knowledge of statistical mechanics, quantum mechanics, and linear operators on Hilbert spaces.

Download or read book J UCS The Journal of Universal Computer Science written by Hermann Maurer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 866 pages. Available in PDF, EPUB and Kindle. Book excerpt: J.UCS is the electronic journal that covers all areas of computer science. The high quality of all accepted papers is ensured by a strict review process and an international editorial board of distinguished computer scientists. The online journal J.UCS is a prototype for modern electronic publishing. Distributed via the Internet, it supports all the search and navigation tools of advanced online systems. This first annual print and CD-ROM archive edition contains all articles published online in J.UCS during 1995. It allows easy and durable access without logging onto the Internet. Uniform citation of papers is guaranteed by identical page numbering and layout of all versions. J.UCS is based on HyperWave (formerly Hyper-G), a networked hypermedia information system compatible with other systems.

Download or read book Kolmogorov Complexity and Algorithmic Randomness written by A. Shen and published by American Mathematical Society. This book was released on 2022-05-18 with total page 511 pages. 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.

Download or read book Computer Science Theory and Applications written by Alexander Kulikov and published by Springer Science & Business Media. This book was released on 2011-06-03 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 6th International Computer Science Symposium in Russia, CSR 2011, held in St. Petersburg, Russia, in June 2011. The 29 papers presented were carefully reviewed and selected from 76 submissions. The scope of topics of the symposium was quite broad and covered basically all areas of the foundations of theoretical computer science.

Download or read book Automata Languages and Programming written by Susanne Albers and published by Springer Science & Business Media. This book was released on 2009-07-06 with total page 808 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Information Theoretic Security written by Yvo Desmedt and published by Springer. This book was released on 2009-11-02 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-conference proceedings of the Second International Conference on Information Theoretic Security, ICITS 2007, held in Madrid, Spain, in May 2007. The 13 revised full papers presented in this volume were carefully reviewed and selected from 26 submissions. There were one invited keynote speech and 3 invited talks to the conference. The topics covered are authentication, group cryptography, private and reliable message transmission, secret sharing, and applications of information theory.

Download or read book Information and Randomness written by Cristian Calude and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.

Download or read book Computer Aided Systems Theory EUROCAST 2001 written by Roberto Moreno-Diaz and published by Springer. This book was released on 2003-08-14 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of CAST as Computer Aided Systems Theory, was introduced by F. Pichler in the late 1980s to include those computer theoretical and practical developments as tools to solve problems in System Science. It was considered as the third component (the other two being CAD and CAM) necessary to build the path from Computer and Systems Sciences to practical developments in Science and Engineering. The University of Linz organized the first CAST workshop in April 1988, which demonstrated the acceptance of the concepts by the scientific and technical community. Next, the University of Las Palmas de Gran Canaria joined the University of Linz to organize the first international meeting on CAST, (Las Palmas, February 1989), under the name EUROCAST’89. This was a very successful gathering of systems theorists, computer scientists, and engineers from most European countries, North America, and Japan. It was agreed that EUROCAST international conferences would be organized every two years, alternating between Las Palmas de Gran Canaria and a continental European location. Thus, successive EUROCAST meetings have taken place in Krems (1991), Las Palmas (1993), Innsbruck (1995), Las Palmas (1997), and Vienna (1999), in addition to an extra-European CAST Conference in Ottawa in 1994.

Download or read book Theory of Information written by Mark Burgin and published by World Scientific. This book was released on 2010 with total page 689 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a fresh approach to scientific understanding of information phenomena. Based on an analysis of information processes in nature, technology, and society, as well as on the main directions in information theory, this book offers a theory that synthesizes various directions into a unified system.

Download or read book Mathematical Linguistics written by Andras Kornai and published by Springer Science & Business Media. This book was released on 2007-12-16 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Linguistics introduces the mathematical foundations of linguistics to computer scientists, engineers, and mathematicians interested in natural language processing. The book presents linguistics as a cumulative body of knowledge from the ground up: no prior knowledge of linguistics is assumed. As the first textbook of its kind, this book is useful for those in information science and in natural language technologies.

Download or read book Algorithms and Complexity written by Bozzano G Luisa and published by Elsevier. This book was released on 1990-09-12 with total page 1014 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first part presents chapters on models of computation, complexity theory, data structures, and efficient computation in many recognized sub-disciplines of Theoretical Computer Science.

Download or read book Information and Randomness written by Cristian S. Calude and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of the monograph Information and Randomness: An Algorithmic Perspective by Crist ian Calude was published in 1994. In my Foreword I said: "The research in algorithmic information theory is already some 30 years old. However, only the recent years have witnessed a really vigorous growth in this area. . . . The present book by Calude fits very well in our series. Much original research is presented. . . making the approach richer in consequences than the classical one. Remarkably, however, the text is so self-contained and coherent that the book may also serve as a textbook. All proofs are given in the book and, thus, it is not necessary to consult other sources for classroom instruction. " The vigorous growth in the study of algorithmic information theory has continued during the past few years, which is clearly visible in the present second edition. Many new results, examples, exercises and open prob lems have been added. The additions include two entirely new chapters: "Computably Enumerable Random Reals" and "Randomness and Incom pleteness". The really comprehensive new bibliography makes the book very valuable for a researcher. The new results about the characterization of computably enumerable random reals, as well as the fascinating Omega Numbers, should contribute much to the value of the book as a textbook. The author has been directly involved in these results that have appeared in the prestigious journals Nature, New Scientist and Pour la Science.