Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Trading information complexity for error   We consider the standard two-party communication model. The central problem
studied in this article is how much one can save in information complexity by
allowing an error of $\epsilon$.
  For arbitrary functions, we obtain lower bounds and upper bounds indicating a
gain that is of order $\Omega(h(\epsilon))$ and $O(h(\sqrt{\epsilon}))$. Here
$h$ denotes the binary entropy function. We analyze the case of the two-bit AND
function in detail to show that for this function the gain is
$\Theta(h(\epsilon))$. This answers a question of [M. Braverman, A. Garg, D.
Pankratov, and O. Weinstein, From information to exact communication (extended
abstract), STOC'13].
  We obtain sharp bounds for the set disjointness function of order $n$. For
the case of the distributional error, we introduce a new protocol that achieves
a gain of $\Theta(\sqrt{h(\epsilon)})$ provided that $n$ is sufficiently large.
We apply these results to answer another of question of Braverman et al.
regarding the randomized communication complexity of the set disjointness
function.
  Answering a question of [Mark Braverman, Interactive information complexity,
STOC'12], we apply our analysis of the set disjointness function to establish a
gap between the two different notions of the prior-free information cost. This
implies that amortized randomized communication complexity is not necessarily
equal to the amortized distributional communication complexity with respect to
the hardest distribution.

18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an