Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Variations on Muchnik's Conditional Complexity Theorem   Muchnik's theorem about simple conditional descriptions states that for all
strings $a$ and $b$ there exists a short program $p$ transforming $a$ to $b$
that has the least possible length and is simple conditional on $b$. In this
paper we present two new proofs of this theorem. The first one is based on the
on-line matching algorithm for bipartite graphs. The second one, based on
extractors, can be generalized to prove a version of Muchnik's theorem for
space-bounded Kolmogorov complexity.

19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys