27 Open Problems in Kolmogorov Complexity

Kolmogorov complexity in perspective

We survey the diverse approaches to the notion of information content: from Shannon entropy to Kolmogorov complexity. The main applications of Kolmogorov complexity are presented: namely, the mathematical notion of randomness (which goes back to the 60’s with the work of MartinLöf, Schnorr, Chaitin, Levin), and classification, which is a recent idea with provocative implementation by Vitanyi an...

Time - Bounded Kolmogorov Complexity in Complexity Theory

This paper presents one method of using time-bounded Kol-mogorov complexity as a measure of the complexity of sets, and outlines a number of applications of this approach to diierent questions in complexity theory. Connections will be drawn among the following topics: NE predicates, ranking functions, pseudorandom generators, and hierarchy theorems in circuit complexity.

Open problems in number theoretic complexity, II

Kolmogorov Complexity Arguments in Combinatorics

The utility of a Kolmogorov complexity method in combinatorial theory is demonstrated by several examples.

Chapter 19 Kolmogorov Complexity

Kolmogorov complexity has intellectual roots in the areas of information theory, computability theory and probability theory. Despites its remarkably simple basis, it has some striking applications in Complexity Theory. The subject was developed by the Russian mathematician Andrei N. Kolmogorov (1903–1987) as an approach to the notion of random sequences and to provide an algorithmic approach t...