Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal Unateness Testers for Real-Valued Functions: Adaptivity Helps   We study the problem of testing unateness of functions $f:\{0,1\}^d \to
\mathbb{R}.$ We give a $O(\frac{d}{\epsilon} \cdot
\log\frac{d}{\epsilon})$-query nonadaptive tester and a
$O(\frac{d}{\epsilon})$-query adaptive tester and show that both testers are
optimal for a fixed distance parameter $\epsilon$. Previously known unateness
testers worked only for Boolean functions, and their query complexity had worse
dependence on the dimension both for the adaptive and the nonadaptive case.
Moreover, no lower bounds for testing unateness were known. We also generalize
our results to obtain optimal unateness testers for functions $f:[n]^d \to
\mathbb{R}$.
  Our results establish that adaptivity helps with testing unateness of
real-valued functions on domains of the form $\{0,1\}^d$ and, more generally,
$[n]^d$. This stands in contrast to the situation for monotonicity testing
where there is no adaptivity gap for functions $f:[n]^d \to \mathbb{R}$.

7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th