Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solovay functions and their applications in algorithmic randomness   Classical versions of Kolmogorov complexity are incomputable. Nevertheless,
in 1975 Solovay showed that there are computable functions $f > K+O(1)$ such
that for infinitely many strings $\sigma$, $f(\sigma)=K(\sigma)+O(1)$, where
$K$ denotes prefix-free Kolmogorov complexity (while $C$ denotes plain
Kolmogorov complexity). Such an $f$ is now called a Solovay function. We prove
that many classical results about $K$ can be obtained by replacing $K$ by a
Solovay function. For example, the three following properties of a function $g$
all hold for the function $K$.
  (i) The sum of the terms $\sum_n 2^{-g(n)}$ is a Martin-L\"of random real.
  (ii) A sequence A is Martin-L\"of random if and only if $C(A \upharpoonright
n) > n -g(n)-O(1)$.
  (iii) A sequence A is K-trivial if and only if $K(A \upharpoonright n) < g(n)
+ O(1)$.
  We show that when fixing any of these three properties, then among all
computable functions exactly the Solovay functions possess this property.
Furthermore, this characterization extends accordingly to the larger class of
right-c.e. functions.

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The categories of this paper are: q-alg
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
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The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio