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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.
| Clasificación: | Libro Electrónico |
|---|---|
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore ; Hackensack, NJ :
World Scientific,
©2007.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.