Chaitin, the inventor of algorithmic information theory, presents in this book the strongest possible version of Goedel'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.
Reihe
Sprache
Verlagsort
Zielgruppe
Produkt-Hinweis
Illustrationen
Worked examples or Exercises
Maße
Höhe: 246 mm
Breite: 189 mm
Dicke: 11 mm
Gewicht
ISBN-13
978-0-521-61604-1 (9780521616041)
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Schweitzer Klassifikation
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.
