Algorithmic Information Theory
by Gregory. J. Chaitin
Publisher: Cambridge University Press 2003
Number of pages: 236
The aim of this book is to present 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 Omega, the halting probability of a universal computer if its program is chosen by tossing a coin. The other half of the book is concerned with encoding Omega as an algebraic equation in integers, a so-called exponential diophantine equation. Although the ideas in this book are not easy, this book has tried to present the material in the most concrete and direct fashion possible. It gives many examples, and computer programs for key algorithms. In particular, the theory of program-size in LISP presented in Chapter 5 and Appendix B, which has not appeared elsewhere, is intended as an illustration of the more abstract ideas in the following chapters.
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by Alexander Shen - arXiv.org
Algorithmic information theory studies description complexity and randomness. This text covers the basic notions of algorithmic information theory: Kolmogorov complexity, Solomonoff universal a priori probability, effective Hausdorff dimension, etc.
by John Watrous - University of Calgary
The focus is on the mathematical theory of quantum information. We will begin with basic principles and methods for reasoning about quantum information, and then move on to a discussion of various results concerning quantum information.
Data compression is useful in some situations because 'compressed data' will save time (in reading and on transmission) and space if compared to the unencoded information it represent. In this book, we describe the decompressor first.
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