An Introduction to Kolmogorov Complexity and Its Applications

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Author: Ming Li,Paul M.B. Vitányi

Publisher: Springer Science & Business Media

ISBN: 9780387498201

Category: Mathematics

Page: 792

View: 1258

“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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Author: Bernd Reusch

Publisher: Springer

ISBN: N.A

Category: Computers

Page: 248

View: 8085

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

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

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Author: Artur Czumaj,Kurt Mehlhorn,Andrew Pitts,Roger Wattenhofer

Publisher: Springer

ISBN: 3642315941

Category: Computers

Page: 860

View: 3846

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

An Algorithmic Perspective

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Author: Cristian S. Calude

Publisher: Springer Science & Business Media

ISBN: 9783540434665

Category: Mathematics

Page: 468

View: 3669

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.

Computer Science Logic

17th International Workshop, CSL 2003, 12th Annual Conference of the EACSL, and 8th Kurt Gödel Colloquium, KGC 2003, Vienna, Austria, August 25-30, 2003, Proceedings

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Author: Matthias Baaz,Johann M. Makowsky

Publisher: Springer

ISBN: 3540452206

Category: Mathematics

Page: 596

View: 1899

This book constitutes the joint refereed proceedings of the 17th International Workshop on Computer Science Logic, CSL 2003, held as the 12th Annual Conference of the EACSL and of the 8th Kurt Gödel Colloquium, KGC 2003 in Vienna, Austria, in August 2003. The 30 revised full papers presented together with abstracts of 9 invited presentations were carefully reviewed and selected from a total of 112 submissions. All current aspects of computer science logic are addressed ranging from mathematical logic and logical foundations to the application of logics in various computing aspects.

Numbers, Information and Complexity

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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: 9751

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.

Formal Languages, Automata and Numeration Systems 1

Introduction to Combinatorics on Words

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Author: Michel Rigo

Publisher: John Wiley & Sons

ISBN: 1119008220

Category: Computers

Page: 338

View: 2692

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.

The Lightness of Being

Big Questions, Real Answers

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Author: Frank Wilczek

Publisher: Penguin UK

ISBN: 0141927623

Category: Science

Page: 292

View: 6608

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.

Linguistic Nativism and the Poverty of the Stimulus

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Author: Alexander Clark,Shalom Lappin

Publisher: John Wiley & Sons

ISBN: 9781444390551

Category: Language Arts & Disciplines

Page: 264

View: 1690

This unique contribution to the ongoing discussion of language acquisition considers the Argument from the Poverty of the Stimulus in language learning in the context of the wider debate over cognitive, computational, and linguistic issues. Critically examines the Argument from the Poverty of the Stimulus - the theory that the linguistic input which children receive is insufficient to explain the rich and rapid development of their knowledge of their first language(s) through general learning mechanisms Focuses on formal learnability properties of the class of natural languages, considered from the perspective of several learning theoretic models The only current book length study of arguments for the poverty of the stimulus which focuses on the computational learning theoretic aspects of the problem

Art of Computer Programming, Volume 2

Seminumerical Algorithms

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Author: Donald E. Knuth

Publisher: Addison-Wesley Professional

ISBN: 0321635760

Category: Computers

Page: 784

View: 8241

The bible of all fundamental algorithms and the work that taught many of today's software developers most of what they know about computer programming. —Byte, September 1995 I can't begin to tell you how many pleasurable hours of study and recreation they have afforded me! I have pored over them in cars, restaurants, at work, at home... and even at a Little League game when my son wasn't in the line-up. —Charles Long If you think you're a really good programmer... read [Knuth's] Art of Computer Programming... You should definitely send me a resume if you can read the whole thing. —Bill Gates It's always a pleasure when a problem is hard enough that you have to get the Knuths off the shelf. I find that merely opening one has a very useful terrorizing effect on computers. —Jonathan Laventhol The second volume offers a complete introduction to the field of seminumerical algorithms, with separate chapters on random numbers and arithmetic. The book summarizes the major paradigms and basic theory of such algorithms, thereby providing a comprehensive interface between computer programming and numerical analysis. Particularly noteworthy in this third edition is Knuth's new treatment of random number generators, and his discussion of calculations with formal power series.