In this paper we characterize normal sequences and finite-state dimension in terms of the automatic Kolmogorov complexity a priori probability. We show that many known results about dimension, including equivalence between aligned non-aligned normality, Wall's theorem, Piatetski–Shapiro's Champernowne's example number its modifications, equivalences different definitions Agafonov's Schnorr's se...

Many statements from the classic information theory (the theory of Shannon’s entropy) have natural counterparts in the algorithmic information theory (in the framework of Kolmogorov complexity). In this paper we discuss one simple instance of the parallelism between Shannon’s and Kolmogorov’s theories: we prove in the setting of Kolmogorov complexity a version of Wolf’s characterization of admi...

It is shown that the 0-1 Law for recursive logics on nite structures admits an equivalent formulation in terms of Kolmogorov complexity. The new formulation opens the possibility of using the Kolmogorov complexity apparatus to easily derive various properties for nite structures satisfying a given properties. Examples that illustrate this point are provided.

1 From probability theory to Kolmogorov complexity 3 1.1 Randomness and Probability theory . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Intuition of finite random strings and Berry’s paradox . . . . . . . . . . . . 5 1.3 Kolmogorov complexity relative to a function . . . . . . . . . . . . . . . . . 6 1.4 Why binary programs? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.5...

Recently, many results on the computational complexity of sorting algorithms were obtained using Kolmogorov complexity (the incompressibility method). Especially, the usually hard average-case analysis is ammenable to this method. Here we survey such results about Bubblesort, Heapsort, Shellsort, Dobosiewicz-sort, Shakersort, and sorting with stacks and queues in sequential or parallel mode. Es...