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We give a unateness tester for functions of the form f : [n] d → R, where n, d ∈ N and R ⊆ R with query complexity O(d log(max(d,n))). Previously known unateness testers work only for Boolean functions over the domain {0, 1} d. We show that every unateness tester for real-valued functions over hypergrid has query complexity Ω(min{d, |R| 2 }). Consequently,… (More)

- Roksana Baleshzar, Deeparnab Chakrabarty, Ramesh Krishnan S. Pallavoor, Sofya Raskhodnikova, Seshadhri Comandur
- Electronic Colloquium on Computational Complexity
- 2017

We study the problem of testing unateness of functions f : {0, 1} d → R. We give a O(d ε ·log d ε)-query nonadaptive tester and a O(d ε)-query adaptive tester and show that both testers are optimal for a fixed distance parameter ε. Previously known unateness testers worked only for Boolean functions, and their query complexity had worse dependence on the… (More)

A Boolean function $f:\{0,1\}^d \mapsto \{0,1\}$ 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)

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