Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New Bounds for the Garden-Hose Model   We show new results about the garden-hose model. Our main results include
improved lower bounds based on non-deterministic communication complexity
(leading to the previously unknown $\Theta(n)$ bounds for Inner Product mod 2
and Disjointness), as well as an $O(n\cdot \log^3 n)$ upper bound for the
Distributed Majority function (previously conjectured to have quadratic
complexity). We show an efficient simulation of formulae made of AND, OR, XOR
gates in the garden-hose model, which implies that lower bounds on the
garden-hose complexity $GH(f)$ of the order $\Omega(n^{2+\epsilon})$ will be
hard to obtain for explicit functions. Furthermore we study a time-bounded
variant of the model, in which even modest savings in time can lead to
exponential lower bounds on the size of garden-hose protocols.

31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
2
The categories of this paper are: math
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol