Game interpretation of Kolmogorov complexity

Kolmogorov Complexity and Games

In this survey we consider some results on Kolmogorov complexity whose proofs are based on interesting games. The close relation between Recursion theory, whose part is Kolmogorov complexity, and Game theory was revealed by Andrey Muchnik. In [10], he associated with every statement φ of Recursion theory a game Gφ that has the following properties. First, Gφ is a game with complete information ...

Logical operations and Kolmogorov complexity

Conditional Kolmogorov complexity can be understood as the complexity of the problem “ ”, where is the problem “construct ” and is the problem “construct ”. Other logical operations ( ) can be interpreted in a similar way, extending Kolmogorov interpretation of intuitionistic logic and Kleene realizability. This leads to interesting problems in algorithmic information theory. Some of these ques...

Kolmogorov Complexity and Information Theory. With an Interpretation in Terms of Questions and Answers

On the Computational Complexity of the Domination Game

The domination game is played on an arbitrary graph $G$ by two players, Dominator and Staller. It is known that verifying whether the game domination number of a graph is bounded by a given integer $k$ is PSPACE-complete. On the other hand, it is showed in this paper that the problem can be solved for a graph $G$ in $mathcal O(Delta(G)cdot |V(G)|^k)$ time. In the special case when $k=3$ and the...

Descriptive Complexity of Computable Sequences

Our goal is to study the complexity of infinite binary recursive sequences. We introduce several measures of the quantity of information they contain. Some measures are based on size of programs that generate the sequence, the others are based on the Kolmogorov complexity of its finite prefixes. The relations between these complexity measures are established. The most surprising among them are ...