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Information and randomness. An algorithmic perspective. Foreword by Gregory J. Chaitin and Arto Salomaa. 2nd rev. and ext. ed. (English) Zbl 1055.68058
Texts in Theoretical Computer Science. An EATCS Series. Berlin: Springer (ISBN 3-540-43466-6/hbk). xx, 467 p. EUR 49.95/net; £ 35.00; sFr 86.00; $ 54.95 (2002).

For a review of the first edition (1994) see Zbl 0922.68073.

Publisher’s description: The book presents in a mathematical clear way the fundamentals of algorithmic information theory and a few selected applications. This 2nd edition presents new and important results obtained in recent years: the characterization of computably enumerable random reals, the construction of an Omega Number for which ZFC cannot determine any digits, and the first successful attempt to compute the exact values of 64 bits of a specific Omega Number. Finally, the book contains a discussion of some interesting philosophical questions related to randomness and mathematical knowledge.

MSC:
68Q30Algorithmic information theory
03D80Applications of computability and recursion theory
94A15General topics of information theory
68-02Research monographs (computer science)