An O~(n)\widetilde{O}(n) Queries Adaptive Tester for Unateness

preprint2016arXivOpen access

Abstract

We present an adaptive tester for the unateness property of Boolean functions. Given a function f:{0,1}n→{0,1}f:\{0,1\}^n \to \{0,1\} the tester makes O(nlog⁡(n)/ε)O(n \log(n)/ε) adaptive queries to the function. The tester always accepts a unate function, and rejects with probability at least 0.9 if a function is εε-far from being unate.

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