Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the communication complexity of XOR functions   An XOR function is a function of the form g(x,y) = f(x + y), for some boolean
function f on n bits. We study the quantum and classical communication
complexity of XOR functions. In the case of exact protocols, we completely
characterise one-way communication complexity for all f. We also show that,
when f is monotone, g's quantum and classical complexities are quadratically
related, and that when f is a linear threshold function, g's quantum complexity
is Theta(n). More generally, we make a structural conjecture about the Fourier
spectra of boolean functions which, if true, would imply that the quantum and
classical exact communication complexities of all XOR functions are
asymptotically equivalent. We give two randomised classical protocols for
general XOR functions which are efficient for certain functions, and a third
protocol for linear threshold functions with high margin. These protocols
operate in the symmetric message passing model with shared randomness.

32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga