Algorithmic Information Theory

Expounds Gödel's incompleteness theorey using an information theoretic approach based on the size of computer programs.

Gregory. J. Chaitin (Author)

9780521616041, Cambridge University Press

Paperback, published 2 December 2004

192 pages
24.6 x 18.8 x 2 cm, 0.345 kg

Chaitin, the inventor of algorithmic information theory, presents in this book the strongest possible version of Gödel'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.

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.

Subject Areas: Mathematical theory of computation [UYA]