Algorithmic Randomness and Complexity
by R. G. Downey, D. R. Hirschfeldt
Publisher: Springer 2010
Number of pages: 629
Computability and complexity theory are two central areas of research in theoretical computer science. This book provides a systematic, technical development of algorithmic randomness and complexity for scientists from diverse fields.
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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 Johan Håstad
This set of notes gives the broad picture of modern complexity theory, defines the basic complexity classes, gives some examples of each complexity class and proves the most standard relations. The author emphasizes the ideas involved in the proofs.
by Karl Petersen - University of North Carolina
These notes provide an introduction to the subject of measure-preserving dynamical systems, discussing the dynamical viewpoint; how and from where measure-preserving systems arise; the construction of measures and invariant measures; etc.
by Avi Wigderson - Princeton University Press
The book provides a broad, conceptual overview of computational complexity theory -- the mathematical study of efficient computation. It is useful for undergraduate and graduate students in mathematics, computer science, and related fields.