Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear list-approximation for short programs (or the power of a few
  random bits)   A $c$-short program for a string $x$ is a description of $x$ of length at
most $C(x) + c$, where $C(x)$ is the Kolmogorov complexity of $x$. We show that
there exists a randomized algorithm that constructs a list of $n$ elements that
contains a $O(\log n)$-short program for $x$. We also show a polynomial-time
randomized construction that achieves the same list size for $O(\log^2
n)$-short programs. These results beat the lower bounds shown by Bauwens et al.
\cite{bmvz:c:shortlist} for deterministic constructions of such lists. We also
prove tight lower bounds for the main parameters of our result. The
constructions use only $O(\log n)$ ($O(\log^2 n)$ for the polynomial-time
result) random bits . Thus using only few random bits it is possible to do
tasks that cannot be done by any deterministic algorithm regardless of its
running time.

31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
2
The categories of this paper are: math
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex