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 ...

C. Calude, A. Nies, L. Staiger, and F. Stephan posed the following question about the relation between plain and prefix Kolmogorov complexities (see their paper in DLT 2008 conference proceedings): does the domain of every optimal decompressor contain the domain of some optimal prefix-free decompressor? In this paper we provide a negative answer to this question.

This paper initiates the study of sets in Euclidean space R (n ≥ 2) that are defined in terms of the dimensions of their elements. Specifically, given an interval I ⊆ [0, 1], we are interested in the connectivity properties of the set DIM consisting of all points in R whose (constructive Hausdorff) dimensions lie in the interval I. It is easy to see that the sets DIM and DIM(n−1,n] are totally ...

Recently, Moser and Tardos [MT10] came up with a constructive proof of the Lovász Local Lemma. In this paper, we give another constructive proof of the lemma, based on Kolmogorov complexity. Actually, we even improve the Local Lemma slightly.

Information distance can be defined not only between two strings but also in a finite multiset of strings of cardinality greater than two. We give an elementary proof for expressing the information distance in conditional Kolmogorov complexity. It is exact since the lower bound equals the upper bound up to a constant additive term.

We revisit the notion of computational depth and sophistication for infinite sequences and study the density of the sets of deep and sophisticated infinite sequences. Koppel defined the sophistication of an object as the length of the shortest total program that given some data as input produces it and the sum of the size of the program with the size of the data is as consice as the smallest de...

The proofs of Chaitin and Boolos for Gödel’s Incompleteness Theorem are studied from the perspectives of constructibility and Rosserizability. By Rosserization of a proof we mean that the independence of the true but unprovable sentence can be shown by assuming only the (simple) consistency of the theory. It is known that Gödel’s own proof for his incompleteness theorem is not Rosserizable, and...

If the influence of visual-motor integration (copying forms) on the quality of handwriting has been widely investigated, the influence of eye-hand coordination (tracing item) has been less well analyzed. The Concise Assessment Scale for Children’s Handwriting (BHK), the Developmental Test of Visual Perception (DTVP-2), and the section “Manual Dexterity” of the Movement Assessment Battery for Ch...

Recently, Moser and Tardos [MT10] came up with a constructive proof of the Lovász Local Lemma. In this paper, we give another constructive proof of the lemma, based on Kolmogorov complexity. Actually, we even improve the Local Lemma slightly.

We present a systematic study of the dynamical scaling process leading to the establishment of the Kolmogorov-Zakharov (KZ) spectrum in weak three-wave turbulence. In the finite-capacity case, in which the transient spectrum reaches infinite frequency in finite time, the dynamical scaling exponent is anomalous in the sense that it cannot be determined from dimensional considerations. As a conse...