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

Format:

Book

Contributor:

Calude, Cristian, 1952-

Chaitin, Gregory J.

Language:

English

Subjects (All):

Kolmogorov complexity.

Computational complexity.

Stochastic processes.

Physical Description:

1 online resource (466 p.)

Edition:

1st ed.

Place of Publication:

Singapore ; Hackensack, NJ : World Scientific, c2007.

Language Note:

English

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. <i>Sample Chapter(s)</i><br>Chapter 1: On Random and Hard-to-Describe Numbers (902 KB)<br> <br><i>Contents:</i><ul><li>On Random and Hard-to-Describe Numbers <i>(C H Bennett)</i></li><li>The Implications of a Cosmological Information Bound for Complexity, Quantum Information and the Nature of Physical Law <i>(P C W Davies)</i></li><li>What is a Computation? <

Contents:

Contents; Preface; Technical Contributions; 1. On Random and Hard-to-Describe Numbers Charles H. Bennett; 1. Berry's Paradox and the Unprovability of Randomness; 2. The Search for a "Random" Real Number; References; 2. Computing Beyond Classical Logic: SVD Computation in Nonassociative Dickson Algebras Francoise Chaitin-Chatelin; 2.1. Introduction; 2.2. Nonassociativity of multiplication; 2.3. Nonassociative Dickson algebras; 2.3.1. Presentation of Dickson's doubling process; 2.3.2. Alternative vectors in Ak, k 4; 2.3.3. The splitting Ak = CDC;1 Dk, k 2

2.4. SVD computation in Dk and Ak, k 32.4.1. c 2 Dk is doubly pure, k 4.; 2.4.2. Deriving the SVD of a in Ak from that of the tail c in Dk, for k 4; 2.4.3. Nonclassical derivation from c to a, k 3; 2.5. Is the nonclassical SVD derivation absurd?; 2.5.1. The conventional analysis; 2.5.2. Induction and nonclassical singular values; 2.6. Conclusion; Acknowledgement; References; 3. Janus-Faced Physics: On Hilbert's 6th Problem N. C. A. da Costa and F. A. Doria; 3.1. Prologue; 3.2. Hilbert's 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. Janus-faced 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 7.2.1. A three states CA by Banks; 7.3. CA over a hexagonal grid and three states; 7.4. Life automata; 7.4.1. Game of life; 7.4.2. Life without death; 7.5. Reversible models; 7.6. Sandpiles; 7.7. Conclusions; Acknowledgments; References; 8. Chaitin's 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 Hilbert's Tenth Problem

10.3. Expressing Omega Through Diophantine Equations

Notes:

In honour of Gregory Chaitin's 60th birthday.

Includes bibliographical references.

ISBN:

9786611911607

9781281911605

1281911607

9789812770837

9812770836

OCLC:

879025560