Ming Li Paul Vitányi Fourth Edition Page 1 An Introduction to Kolmogorov Complexity and Its
Applications Ming Li Paul Vitányi Fourth Edition Texts in Computer Science Page 2 Texts in …

We consider various mathematical refinements of the notion of randomness of an infinite
sequence and relations between them. On the base of the game approach a new possible …

Abstract CONTENTS Introduction Chapter I. The main notions and facts § 1.1. The notion of
randomness depends on a given probability distribution § 1.2. Three faces of randomness …

The theory of constructive (recursive) models follows from works of Froehlich, Shepherdson,
Mal'tsev, Kuznetsov, Rabin, and Vaught in the 50s. Within the framework of this theory …

In the aftermath of the discoveries in foundations of mathematiC's there was surprisingly little
effect on mathematics as a whole. If one looks at stan dard textbooks in different …

What is an algorithm? The interest in this foundational problem is not only theoretical;
applications include specification, validation and verification of software and hardware …

We attempt to put the title problem and the Church-Turing thesis into a proper perspective
and to clarify some common misconceptions related to Turing's analysis of computation. We …

Church's Thesis asserts that the only numeric functions that can be calculated by effective
means are the recursive ones, which are the same, extensionally, as the Turing-computable …

We suggest a general approach to the notion of computability for the wide variety of classes
of constructive objects which admit a constructive description in formal languages with a …

There are human beings whose intellectual power exceeds that of ordinary men. In my life,
in my personal experience, there were three such men, and one of them was Andrei …