Algorithmic Information Theory (Cambridge Tracts in Theoretical Computer Science No. 1)

Algorithmic Information Theory (Cambridge Tracts in Theoretical Computer Science No. 1)

By: Gregory J. Chaitin (author), C. J. Van Rijsbergen (series_editor), Y. Gurevich (series_editor), S. Abramsky (series_editor), J. W. de Bakker (series_editor), J. V. Tucker (series_editor), P. H. Aczel (series_editor)Paperback

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Description

Chaitin, the inventor of algorithmic information theory, presents in this book the strongest possible version of Godel's incompleteness theorem, using an information theoretic approach based on the size of computer programs. One half of the book is concerned with studying the halting probability of a universal computer if its program is chosen by tossing a coin. The other half is concerned with encoding the halting probability as an algebraic equation in integers, a so-called exponential diophantine equation.

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Contents

Foreword; Preface; Figures; 1. Introduction; Part I. Formalisms for Computation: Register Machines, Exponential Diophantine Equations, and Pure LISP: 2. The arithmetization of register machines; 3. A version of Pure LISP; 4. The LISP interpreter EVAL; Part II. Program Size, Halting Probabilities, Randomness, and Metamathematics: 5. Conceptual development; 6. Program size; 7. Randomness; 8. Incompleteness; 9. Conclusion; Bibliography.

Product Details

  • publication date: 02/12/2004
  • ISBN13: 9780521616041
  • Format: Paperback
  • Number Of Pages: 192
  • ID: 9780521616041
  • weight: 350
  • ISBN10: 0521616042

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