An Introduction to Kolmogorov Complexity and Its Applications

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.

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 computerscience. Included are also numerous problem sets, comments, source references, and hints to solutions of problems. New topics in this edition include Omega numbers, KolmogorovLoveland randomness, universal learning, communication complexity, Kolmogorov's random graphs, time-limited universal distribution, Shannon information and others.

Develops Kolmogorov theory in detail and outlines the wide range of illustrative applications Presents recent, major results in the field; topics include, Omega numbers, Kolmogorov-Loveland randomness, universal learning, communication complexity, Kolmogorov's random graphs, time-limited universal distribution, Shannon information Introduces results from prominent researchers in the field, such as those found by Slaman-Kucera, Downey, Hirschfeldt, Nies, Solovay, Miller and many more Includes applications to hierarchical clustering, phylogeny in genomics, classification of music, Google, and the World Wide Web Additional exercises on new results Improved sections on high-probability properties and Kolmogorov's structure function, information distance Includes supplementary material: sn.pub/extras

Klappentext

This ongoing bestseller, now in its third edition, is considered the standard reference on Kolmogorov complexity, a modern theory of information that is concerned with information in individual objects.

New key features and topics in the 3rd edition:

• New results on randomness

• Kolmogorov's structure function, model selection, and MDL

• Incompressibility method: counting unlabeled graphs, Shellsort, communication complexity

• Derandomization

• Kolmogorov complexity versus Shannon information, rate distortion, lossy compression, denoising

• Theoretical results on information distance

• The similarity metric with applications to genomics, phylogeny, clustering, classification, semantic meaning, question-answer systems

  *Quantum Kolmogorov complexity

  Written by two experts in the field, this book is ideal for advanced undergraduate students, graduate students, and researchers in all fields of science. It is self-contained: it contains the basic requirements from mathematics, probability theory, statistics, information theory, and computer science. Included are history, theory, new developments, a wide range of applications, numerous (new) problem sets, comments, source references, and hints to solutions of problems. This is the only comprehensive treatment of the central ideas of Kolmogorov complexity and their applications.

  ``Li and Vitányi have provided an ideal book for the exploration of a deep, beautiful and important part of computer science.''

  -- Juris Hartmanis, Turing Award Winner 1993, Cornell University, Ithaca, NY.

  ``The book is likely to remain the standard treatment of Kolmogorov complexity for a long time.''

  -- Jorma J. Rissanen, IBM Research, California.

  ``The book of Li and Vitányi is unexcelled.''

  -- Ray J. Solomonoff, Oxbridge Research, Cambridge, Massachusetts

  "The book is outstanding...the authors did their job unbelievably well...necessary reading for all kinds of readers from undergraduate students to top authorities in the field."

  -- Vladimir A. Uspensky and Alexander K. Shen, Journal of Symbolic Logic [Review]

  ``Careful and clear introduction to a subtle and deep field.''

  --David G. Stork, Ricoh Innovations, California, Amazon [Review]

  ``THE book on Kolmogorov Complexity.''

  --Lance Fortnow, University of Chicago, IL, Amazon [Review]

  Inhalt
  Preliminaries.- Algorithmic Complexity.- Algorithmic Prefix Complexity.- Algorithmic Probability.- Inductive Reasoning.- The Incompressibility Method.- Resource-Bounded Complexity.- Physics, Information, and Computation.