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arXiv · 1706.00053

A Lower Bound for Nonadaptive, One-Sided Error Testing of Unateness of Boolean Functions over the Hypercube

Roksana Baleshzar·Deeparnab Chakrabarty·Ramesh Krishnan S. Pallavoor·Sofya Raskhodnikova·C. Seshadhri
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Abstract

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 $Ω(\frac{d}{\log d})$ queries. This result improves upon the $Ω(\frac{d}{\log^2 d})$ lower bound for the same class of testers due to Chen et al. (STOC, 2017).

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Roksana Baleshzar, Deeparnab Chakrabarty, Ramesh Krishnan S. Pallavoor, Sofya Raskhodnikova, C. Seshadhri. 2017-05-31. A Lower Bound for Nonadaptive, One-Sided Error Testing of Unateness of Boolean Functions over the Hypercube. https://arxiv.org/abs/1706.00053

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