Randomness and Completeness in Computational Complexity, Dieter van Melkebeek

Автор: Rodney G. Downey; Denis R. Hirschfeldt
Название: Algorithmic Randomness and Complexity
ISBN: 1493938207 ISBN-13(EAN): 9781493938209
Издательство: Springer
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Цена: 13974.00 р.
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Описание: Exploring the theory of computability and complexity over the real numbers, this book provides a systematic, technical development of "algorithmic randomness" and complexity for scientists working in diverse fields concerned with theoretical computer science.

Автор: Gregory J. Chaitin
Название: Exploring RANDOMNESS
ISBN: 1447110854 ISBN-13(EAN): 9781447110859
Издательство: Springer
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Цена: 15372.00 р.
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Описание: This essential companion to Chaitin`s successful books The Unknowable and The Limits of Mathematics, presents the technical core of his theory of program-size complexity. The LISP code for this book is available at the author`s Web site together with a Java applet LISP interpreter.

Автор: Cristian S. Calude
Название: Information and Randomness
ISBN: 3642077935 ISBN-13(EAN): 9783642077937
Издательство: Springer
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Цена: 11173.00 р.
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Описание: 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.