An Introduction to Kolmogorov Complexity and Its Applications

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An Introduction to Kolmogorov Complexity and Its Applications

An Introduction to Kolmogorov Complexity and Its Applications

  • Author: Ming Li,Paul Vitanyi
  • Publisher: Springer Science & Business Media
  • ISBN: 1475726066
  • Category: Mathematics
  • Page: 637
  • View: 3557
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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).

An Introduction to Kolmogorov Complexity and Its Applications

This ebook list for those who looking for to read An Introduction to Kolmogorov Complexity and Its Applications, you can read or download in PDF, ePub or Mobi. May some of ebooks not available on your country and only available for those who subscribe and depend to the source of library websites.

An Introduction to Kolmogorov Complexity and Its Applications

An Introduction to Kolmogorov Complexity and Its Applications

  • Author: Ming Li,Paul M.B. Vitányi
  • Publisher: Springer Science & Business Media
  • ISBN: 9780387498201
  • Category: Mathematics
  • Page: 792
  • View: 6889
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“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.

An Introduction to Kolmogorov Complexity and Its Applications

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An Introduction to Kolmogorov Complexity and Its Applications

An Introduction to Kolmogorov Complexity and Its Applications

  • Author: Bernd Reusch
  • Publisher: Springer
  • ISBN: N.A
  • Category: Computers
  • Page: 248
  • View: 1347
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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.

Automata, Languages, and Programming

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Automata, Languages, and Programming

Automata, Languages, and Programming

39th International Colloquium, ICALP 2012, Warwick, UK, July 9-13, 2012, Proceedings

  • Author: Artur Czumaj,Kurt Mehlhorn,Andrew Pitts,Roger Wattenhofer
  • Publisher: Springer
  • ISBN: 3642315941
  • Category: Computers
  • Page: 860
  • View: 9478
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This two-volume set of LNCS 7391 and LNCS 7392 constitutes the refereed proceedings of the 39th International Colloquium on Automata, Languages and Programming, ICALP 2012, held in Warwick, UK, in July 2012. The total of 123 revised full papers presented in this volume were carefully reviewed and selected from 432 submissions. They are organized in three tracks focussing on algorithms, complexity and games; logic, semantics, automata and theory of programming; and foundations of networked computation.

Information and Randomness

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Information and Randomness

Information and Randomness

An Algorithmic Perspective

  • Author: Cristian S. Calude
  • Publisher: Springer Science & Business Media
  • ISBN: 9783540434665
  • Category: Mathematics
  • Page: 468
  • View: 5198
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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.

Numbers, Information and Complexity

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Numbers, Information and Complexity

Numbers, Information and Complexity

  • Author: Ingo Althöfer,Ning Cai,Gunter Dueck,Levon H. Khachatrian,Marcus Pinsker,G. Sarkozy,Ingo Wegener,Zhen Zhang
  • Publisher: Springer Science & Business Media
  • ISBN: 9780792377658
  • Category: Technology & Engineering
  • Page: 652
  • View: 4870
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Numbers, Information and Complexity is a collection of about 50 articles in honour of Rudolf Ahlswede. His main areas of research are represented in the three sections, `Numbers and Combinations', `Information Theory (Channels and Networks, Combinatorial and Algebraic Coding, Cryptology, with the related fields Data Compression, Entropy Theory, Symbolic Dynamics, Probability and Statistics)', and `Complexity'. Special attention was paid to the interplay between the fields. Surveys on topics of current interest are included as well as new research results. The book features surveys on Combinatorics about topics such as intersection theorems, which are not yet covered in textbooks, several contributions by leading experts in data compression, and relations to Natural Sciences are discussed.

Algorithmic Learning Theory

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Algorithmic Learning Theory

Algorithmic Learning Theory

8th International Workshop, ALT '97, Sendai, Japan, October 6-8, 1997. Proceedings

  • Author: Ming Li
  • Publisher: Springer Science & Business Media
  • ISBN: 9783540635772
  • Category: Computers
  • Page: 460
  • View: 9171
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This book constitutes the strictly refereed post-workshop proceedings of the Second International Workshop on Database Issues for Data Visualization, held in conjunction with the IEEE Visualization '95 conference in Atlanta, Georgia, in October 1995. Besides 13 revised full papers, the book presents three workshop subgroup reports summarizing the contents of the book as well as the state-of-the-art in the areas of scientific data modelling, supporting interactive database exploration, and visualization related metadata. The volume provides a snapshop of current research in the area and surveys the problems that must be addressed now and in the future towards the integration of database management systems and data visualization.

The Lightness of Being

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The Lightness of Being

The Lightness of Being

Big Questions, Real Answers

  • Author: Frank Wilczek
  • Publisher: Penguin UK
  • ISBN: 0141927623
  • Category: Science
  • Page: 292
  • View: 319
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What's the meaning of it all? Or rather: what exactly is 'it'? Here Frank Wilczek, Nobel Prize-winning physicist and legend, examines the very nature of reality itself, showing how almost everything we think we know about 'it' is wrong. The Lightness of Being is an engaging tour de force, revealing a universe where matter is the hum of strange music, mass doesn't weigh, and empty space is a multilayered, multicoloured superconductor. Physicists' understanding of the essential nature of reality changed radically over the past quarter century. And Frank Wilczek has played a lead role in establishing the new paradigms. Transcending the clash and mismatch of older ideas about what matter and space is, Wilczek presents some brilliant and clear syntheses. Extraordinarily readable and authoritative, The Lightness of Being is the first book to unwrap these exciting new ideas for the general public. It explores their implications for basic questions about space, mass, energy, and the longed-for possibility of a fully unified theory of Nature. Pointing to new directions where great discoveries in fundamental physics are likely, and providing a visionary context for the experiments in CERN, he envisions a new Golden Age in physics.

Formal Languages, Automata and Numeration Systems 1

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Formal Languages, Automata and Numeration Systems 1

Formal Languages, Automata and Numeration Systems 1

Introduction to Combinatorics on Words

  • Author: Michel Rigo
  • Publisher: John Wiley & Sons
  • ISBN: 1119008220
  • Category: Computers
  • Page: 338
  • View: 1083
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Formal Languages, Automaton and Numeration Systems presents readers with a review of research related to formal language theory, combinatorics on words or numeration systems, such as Words, DLT (Developments in Language Theory), ICALP, MFCS (Mathematical Foundation of Computer Science), Mons Theoretical Computer Science Days, Numeration, CANT (Combinatorics, Automata and Number Theory). Combinatorics on words deals with problems that can be stated in a non-commutative monoid, such as subword complexity of finite or infinite words, construction and properties of infinite words, unavoidable regularities or patterns. When considering some numeration systems, any integer can be represented as a finite word over an alphabet of digits. This simple observation leads to the study of the relationship between the arithmetical properties of the integers and the syntactical properties of the corresponding representations. One of the most profound results in this direction is given by the celebrated theorem by Cobham. Surprisingly, a recent extension of this result to complex numbers led to the famous Four Exponentials Conjecture. This is just one example of the fruitful relationship between formal language theory (including the theory of automata) and number theory.