Randomness and complexity : from Leibniz to Chaitin /
The book is a collection of papers written by a selection of eminent authors from around the world in honour of Gregory Chaitin's 60th birthday. This is a unique volume including technical contributions, philosophical papers and essays.
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| Other Authors: | , |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Singapore ; Hackensack, NJ :
World Scientific,
2007
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| Subjects: | |
| Local Note: | ProQuest Ebook Central |
MARC
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| 245 | 0 | 0 | |a Randomness and complexity : |b from Leibniz to Chaitin / |c editor, Cristian S. Calude. |
| 260 | |a Singapore ; |a Hackensack, NJ : |b World Scientific, |c ©2007. | ||
| 300 | |a 1 online resource (xviii, 445 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 504 | |a Includes bibliographical references. | ||
| 505 | 0 | |a Cover -- Contents -- Preface -- Technical Contributions -- 1. On Random and Hard-to-Describe Numbers Charles H. Bennett -- 1. Berrys Paradox and the Unprovability of Randomness -- 2. The Search for a 8220;Random Real Number -- References -- 2. Computing Beyond Classical Logic: SVD Computation in Nonassociative Dickson Algebras Fran184;coise Chaitin-Chatelin -- 2.1. Introduction -- 2.2. Nonassociativity of multiplication -- 2.3. Nonassociative Dickson algebras -- 2.4. SVD computation in Dk and Ak, k 3 -- 2.5. Is the nonclassical SVD derivation absurd? -- 2.6. Conclusion -- Acknowledgement -- References -- 3. JanusFaced Physics: On Hilberts 6th Problem N.C.A. da Costa and F.A. Doria -- 3.1. Prologue -- 3.2. Hilberts 6th Problem -- 3.3. A review of axiomatization techniques -- 3.4. Structures, species of structures, models -- 3.5. Axiomatization in mathematics -- 3.6. Suppes predicates for classical field theories in physics -- 3.7. Generalized incompleteness -- 3.8. Higher degrees -- 3.9. The function and the arithmetical hierarchy -- 3.10. First applications: mechanics and chaos theory -- 3.11. Janusfaced physics -- Acknowledgments -- References -- 4. The Implications of a Cosmological Information Bound for Complexity, Quantum Information and the Nature of Physical Law P.C.W. Davies -- 4.1. What are the laws of physics? -- 4.2. Laws as software -- 4.3. The quantum vacuum -- 4.4. Quantum information processing -- 4.5. Unfinished business -- Acknowledgments -- Footnotes -- 5. What Is a Computation? Martin Davis -- The Turing Post Language -- Codes for Turing Post Programs -- The Universal Program -- The Halting Problem -- Other Unsolvable Problems -- Undecidable Statements -- Complexity and Randomness -- Unsolvability of Halting Problem -- An Unsolvable Word Problem -- 6. On the Kolmogorov-Chaitin Complexity for Short Sequences Jean-Paul Delahaye and Hector Zenil -- References -- 7. Circuit Universality of Two Dimensional Cellular Automata: A Review A. Gajardo and E. Goles -- 7.1. Introduction -- 7.2. Computing through signals -- 7.3. CA over a hexagonal grid and three states -- 7.4. Life automata -- 7.5. Reversible models -- 7.6. Sandpiles -- 7.7. Conclusions -- Acknowledgments -- References -- 8. Chaitins Graph Coloring Algorithm James Goodman -- References -- 9. A Berry-type Paradox Gabriele Lolli -- References -- 10. in Number Theory Toby Ord and Tien D. Kieu -- 10.1. Recursive Enumerability, Algorithmic Randomness and -- 10.2. Diophantine Equations and Hilberts Tenth Problem -- 10.3. Expressing Omega Through Diophantine Equations -- References -- 11. The Secret Number. An Exposition of Chaitins Theory Grzegorz Rozenberg and Arto Salomaa -- 11.1. Introduction -- 11.2. Compressibility of information and randomness. An informal discussion -- 11.3. Prefix-freeness and Krafts inequality -- 11.4. Computer: a formal notion -- 11.5. Universal computer -- 11.6. Complexity -- 11.7. Fundamental inequalities -- 11.8. Computational and information-theoretic complexity -- 11.9. Self-delimiting programs -- 11.10. Randomness: intuitive considerations -- 11.11. Probability and complexity -- 11.12. Degree of randomness -- 11.13. Magic bits: pro. | |
| 520 | |a The book is a collection of papers written by a selection of eminent authors from around the world in honour of Gregory Chaitin's 60th birthday. This is a unique volume including technical contributions, philosophical papers and essays. | ||
| 588 | 0 | |a Print version record. | |
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Kolmogorov complexity. | |
| 650 | 0 | |a Computational complexity. | |
| 650 | 0 | |a Stochastic processes. | |
| 700 | 1 | |a Calude, Cristian, |d 1952- |1 https://id.oclc.org/worldcat/entity/E39PBJpPFVbTHK68H4by4Byjmd | |
| 700 | 1 | |a Chaitin, Gregory J. | |
| 758 | |i has work: |a Randomness and complexity (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGvgWDVybxYHqFydmKqwyd |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
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