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The Resource Randomness and complexity : from Leibniz to Chaitin, editor, Cristian S. Calude

Randomness and complexity : from Leibniz to Chaitin, editor, Cristian S. Calude

Contributor
Summary
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
Language
eng
Work
Publication
Extent
1 online resource (xviii, 445 pages)
Contents
  • 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
Isbn
9781281911605
Instance
Label
Randomness and complexity : from Leibniz to Chaitin
Title
Randomness and complexity
Title remainder
from Leibniz to Chaitin
Statement of responsibility
editor, Cristian S. Calude
Contributor
Subject
Genre
Language
eng
Summary
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
Member of
Cataloging source
E7B
Dewey number
519.2
Illustrations
illustrations
Index
no index present
LC call number
QA267.7
LC item number
.R36 2007eb
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorDate
1952-
http://library.link/vocab/relatedWorkOrContributorName
  • Calude, Cristian
  • Chaitin, Gregory J
http://library.link/vocab/subjectName
  • Kolmogorov complexity
  • Computational complexity
  • Stochastic processes
  • MATHEMATICS
  • Computational complexity
  • Kolmogorov complexity
  • Stochastic processes
Label
Randomness and complexity : from Leibniz to Chaitin, editor, Cristian S. Calude
Instantiates
Publication
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Control code
646768478
Dimensions
unknown
Extent
1 online resource (xviii, 445 pages)
Form of item
online
Isbn
9781281911605
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
illustrations
Specific material designation
remote
System control number
(OCoLC)646768478
Label
Randomness and complexity : from Leibniz to Chaitin, editor, Cristian S. Calude
Publication
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Control code
646768478
Dimensions
unknown
Extent
1 online resource (xviii, 445 pages)
Form of item
online
Isbn
9781281911605
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
illustrations
Specific material designation
remote
System control number
(OCoLC)646768478

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Genre

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