Kolmogor complexity and its applications. Vyugin V.V.

The book is designed for initial acquaintance with the basics of the theory of Kolmogor complexity and algorithmic accident. The first part gives the elements of the Shannon theory of information and coding. The second part provides the basic concepts and theorems of the Kolmogor approach to substantiating the theory of probabilities and the theory of information based on the theory of algorithms. The concepts of various types of Kolmogor complexity are introduced and studied: simple, prefix, monotonous complexity, the corresponding dual concept is considered - a priori half -timer. The definition of an infinite sequence random according to Martin-LEF is given, equivalent definitions are studied using Kolmogori complexity. The issues of universal forecasting are considered. The third part contains more complex results that develop the Kolmogorov approach to justifying the theory of probability.

The book is designed for students and graduate students of mathematical and applied mathematical specialties.