Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Automatic Kolmogorov complexity, normality and finite state dimension
  revisited   It is well known that normality can be described as incompressibility via
finite automata. Still the statement and the proof of this result as given by
Becher and Heiber (2013) in terms of "lossless finite-state compressors" do not
follow the standard scheme of Kolmogorov complexity definition (an automaton is
used for compression, not decompression). We modify this approach to make it
more similar to the traditional Kolmogorov complexity theory (and simpler) by
explicitly defining the notion of automatic Kolmogorov complexity and using its
simple properties.
  Using this characterization and a sufficient condition for normality in terms
of Kolmogorov complexity derived from it, we provide easy proofs for classical
results about normal sequences (Champernown, Wall, Piatetski-Shapiro,
Besicovitch, Copeland, Erdos et al.)
  Then we extend this approach to finite state dimension. We show that the
block entropy definition of the finite state dimension remains the same if
non-aligned blocks are used. Then we provide equivalent definitions in terms of
automatic complexity, superadditive bounds for Kolmogorov complexity,
calibrated superadditive functions and finite state a priori probability and
use them to give simple proofs for known results about finite state dimension,
and for Agafonov's result saying that normality is preserved by automatic
selection rules as well as the results of Schnorr and Stimm that relate
normality to finite state martingales.
  Some results of this paper were presented at the Fundamentals in Computing
Theory conferences in 2017 and 2019. Preliminary version of this paper (that
does not mention the finite state dimension) was published in arxiv in~2017
(see the previous version of this submission).

15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat