Khot and Shinkar (RANDOM, 2016) recently describe an adaptive, O(nlog(n)/ε)-query tester for unateness of Boolean functions f:{0,1}n→{0,1}. In this note we describe a simple non-adaptive, O(nlog(n/ε)/ε) -query tester for unateness for functions over the hypercube with any ordered range.
@article{arxiv.1608.06980,
title = {A $\widetilde{O}(n)$ Non-Adaptive Tester for Unateness},
author = {Deeparnab Chakrabarty and C. Seshadhri},
journal= {arXiv preprint arXiv:1608.06980},
year = {2016}
}
Comments
We mention the relation of our algorithm to Levin's investment strategy, as pointed out by Oded Goldreich