Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficiently Testing Sparse GF(2) Polynomials   We give the first algorithm that is both query-efficient and time-efficient
for testing whether an unknown function $f: \{0,1\}^n \to \{0,1\}$ is an
$s$-sparse GF(2) polynomial versus $\eps$-far from every such polynomial. Our
algorithm makes $\poly(s,1/\eps)$ black-box queries to $f$ and runs in time $n
\cdot \poly(s,1/\eps)$. The only previous algorithm for this testing problem
\cite{DLM+:07} used poly$(s,1/\eps)$ queries, but had running time exponential
in $s$ and super-polynomial in $1/\eps$.
  Our approach significantly extends the ``testing by implicit learning''
methodology of \cite{DLM+:07}. The learning component of that earlier work was
a brute-force exhaustive search over a concept class to find a hypothesis
consistent with a sample of random examples. In this work, the learning
component is a sophisticated exact learning algorithm for sparse GF(2)
polynomials due to Schapire and Sellie \cite{SchapireSellie:96}. A crucial
element of this work, which enables us to simulate the membership queries
required by \cite{SchapireSellie:96}, is an analysis establishing new
properties of how sparse GF(2) polynomials simplify under certain restrictions
of ``low-influence'' sets of variables.

32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
2
The categories of this paper are: math
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess