TY  - BOOK
AU  - Shen,A.
AU  - Uspensky,V.A.
AU  - Vereshchagin,N.
TI  - Kolmogorov complexity and algorithmic randomness
T2  - Mathematical surveys and monographs
SN  - 9781470431822 (alk. paper)
U1  - 510MS 23
PY  - 2017///
CY  - Providence : 
PB  - American Mathematical Society
KW  - Kolmogorov complexity
KW  - Computational complexity
KW  - Information theory
N1  - Includes bibliographical references and index; Preface --
 Basic notions and notation --
 Introduction : What is this book about? --
1. Plain Kolmogorov complexity -
2. Complexity of pairs and conditional complexity --
3. Martin-Löf randomness --
4. A priori probability and prefix complexity --
5. Monotone complexity --
6. General scheme for complexities --
7. Shannon entropy and Kolmogorov complexity --
8. Some applications --
9. Frequency and game approaches to randomness --
10. Inequalities for entropy, complexity, and size --
11. Common information --
12. Multisource algorithmic information theory --
13. Information and logic --
14. Algorithmic statistics --
Appendix 1. Complexity and foundations of probability --
Appendix 2. Four algorithmic faces of randomness
N2  - This edition reprints in one volume the second edition of this title, which was published in three volumes by The MIT Press in 1969. The original edition was published in 1964, translated from the Russian. Eighteen Russian mathematicians survey the scope of math, from elementary to the advanced levels, writing to educate a lay audience those with "secondary school mathematics" who are motivated to know more. Discussion includes both the origins and the development of analytic geometry, algebra, ordinary differential equations, partial differential equations, curve and surface theories, prime numbers, probability, functions of a complex variable, linear algebra, non-Euclidean geometry, topology, functional analysis, and groups and other algebraic systems
ER  -