Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a conditional inequality in Kolmogorov complexity and its
  applications in communication complexity   Romashchenko and Zimand~\cite{rom-zim:c:mutualinfo} have shown that if we
partition the set of pairs $(x,y)$ of $n$-bit strings into combinatorial
rectangles, then $I(x:y) \geq I(x:y \mid t(x,y)) - O(\log n)$, where $I$
denotes mutual information in the Kolmogorov complexity sense, and $t(x,y)$ is
the rectangle containing $(x,y)$. We observe that this inequality can be
extended to coverings with rectangles which may overlap. The new inequality
essentially states that in case of a covering with combinatorial rectangles,
  $I(x:y) \geq I(x:y \mid t(x,y)) - \log \rho - O(\log n)$, where $t(x,y)$ is
any rectangle containing $(x,y)$ and $\rho$ is the thickness of the covering,
which is the maximum number of rectangles that overlap. We discuss applications
to communication complexity of protocols that are nondeterministic, or
randomized, or Arthur-Merlin, and also to the information complexity of
interactive protocols.

12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an