Khot and Shinkar (RANDOM, 2016) recently describe an adaptive, $O(n\log(n)/\varepsilon)$-query tester for unateness of Boolean functions $f:\{0,1\}^n \mapsto \{0,1\}$. In this note we describe a simple non-adaptive, $O(n\log(n/\varepsilon)/\varepsilon)$ -query tester for unateness for functions over the hypercube with any ordered range.
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 ... more >>>
A Boolean function $f:\{0,1\}^d \to \{0,1\}$ is unate if, along each coordinate, the function is either nondecreasing or nonincreasing. In this note, we prove that any nonadaptive, one-sided error unateness tester must make $\Omega(\frac{d}{\log d})$ queries. This result improves upon the $\Omega(\frac{d}{\log^2 d})$ lower bound for the same class of ... more >>>
