Algorithmic Information Theory

Gregory. J. Chaitin

doi:10.1017/CBO9780511608858

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.

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Algorithmic Information Theory

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Foreword
pp vii-viii

Preface
pp ix-x

Figures
pp xi-xii

1 - Introduction
pp 1-5

I - Formalisms for Computation: Register Machines, Exponential Diophantine Equations, & Pure LISP
pp 6-6

2 - The Arithmetization of Register Machines
pp 7-50

3 - A Version of Pure LISP
pp 51-68

4 - The LISP Interpreter EVAL
pp 69-90

II - Program Size, Halting Probabilities, Randomness, & Metamathematics
pp 91-91

5 - Conceptual Development
pp 92-106

6 - Program Size
pp 107-127

7 - Randomness
pp 128-145

8 - Incompleteness
pp 146-162

9 - Conclusion
pp 163-164

A - Implementation Notes
pp 165-166

B - The Number of S-expressions of Size N
pp 167-175

Bibliography
pp 176-178

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Algorithmic Information Theory

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