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Author: Rodney G. Downey
Publisher: Springer Science & Business Media
Published: 2010-10-29
Total Pages: 883
ISBN-13: 0387684417
DOWNLOAD EBOOKComputability 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.
Author: Cristian Calude
Publisher: World Scientific
Published: 2007
Total Pages: 466
ISBN-13: 9812770828
DOWNLOAD EBOOKThe book is a collection of papers written by a selection of eminent authors from around the world in honour of Gregory Chaitin's 60th birthday. This is a unique volume including technical contributions, philosophical papers and essays.
Author: Ming Li
Publisher: Springer Science & Business Media
Published: 2013-03-09
Total Pages: 655
ISBN-13: 1475726066
DOWNLOAD EBOOKBriefly, 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).
Author: Frédérique Bassino
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2020-06-08
Total Pages: 386
ISBN-13: 3110667029
DOWNLOAD EBOOKThis book shows new directions in group theory motivated by computer science. It reflects the transition from geometric group theory to group theory of the 21st century that has strong connections to computer science. Now that geometric group theory is drifting further and further away from group theory to geometry, it is natural to look for new tools and new directions in group theory which are present.
Author: A. Shen
Publisher: American Mathematical Soc.
Published: 2017-11-02
Total Pages: 534
ISBN-13: 1470431823
DOWNLOAD EBOOKLooking 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.
Author: Cristian Calude
Publisher: Springer Science & Business Media
Published: 2013-03-09
Total Pages: 252
ISBN-13: 3662030497
DOWNLOAD EBOOK"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.
Author: Michael Strevens
Publisher: Harvard University Press
Published: 2003-06-30
Total Pages: 446
ISBN-13: 9780674010420
DOWNLOAD EBOOKMichael Strevens shows how simplicity can co-exist with the tangled interconnections within complex systems. By looking at the foundations of statistical reasoning about complex systems (gases, ecosystems and even social systems) he provides an understanding of how simplicity emerges from complexity.
Author: Manfred Denker
Publisher: Springer Science & Business Media
Published: 1998-11-01
Total Pages: 550
ISBN-13: 9780817640316
DOWNLOAD EBOOKIntegrates traditional statistical data analysis with new computational experimentation capabilities and concepts of algorithmic complexity and chaotic behavior in nonlinear dynamic systems, offering tools for the study of random phenomena occurring in engineering and the natural, life, and social sciences. Each chapter presents experiments, exercises, and projects using the Mathematica Uncertain Virtual Worlds software packages. Large and original real-life data sets are introduced and analyzed as a model for independent study. Includes brief tutorials on using Mathematica programs. Intended as a text for an introductory level statistics course. Prerequisites include calculus and basic computer programming. Annotation copyrighted by Book News, Inc., Portland, OR
Author: Bernard Chazelle
Publisher: Cambridge University Press
Published: 2000
Total Pages: 500
ISBN-13: 9780521003575
DOWNLOAD EBOOKThe discrepancy method is the glue that binds randomness and complexity. It is the bridge between randomized computation and discrepancy theory, the area of mathematics concerned with irregularities in distributions. The discrepancy method has played a major role in complexity theory; in particular, it has caused a mini-revolution of sorts in computational geometry. This book tells the story of the discrepancy method in a few short independent vignettes. It is a varied tale which includes such topics as communication complexity, pseudo-randomness, rapidly mixing Markov chains, points on the sphere and modular forms, derandomization, convex hulls, Voronoi diagrams, linear programming and extensions, geometric sampling, VC-dimension theory, minimum spanning trees, linear circuit complexity, and multidimensional searching. The mathematical treatment is thorough and self-contained. In particular, background material in discrepancy theory is supplied as needed. Thus the book should appeal to students and researchers in computer science, operations research, pure and applied mathematics, and engineering.
Author: Mark Burgin
Publisher: World Scientific
Published: 2016-11-28
Total Pages: 410
ISBN-13: 9813109041
DOWNLOAD EBOOKThe 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.
