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Boolean Unateness Testing with Õ(n^{3/4}) Adaptive Queries | IEEE Conference Publication | IEEE Xplore

Boolean Unateness Testing with Õ(n^{3/4}) Adaptive Queries


Abstract:

We give an adaptive algorithm that tests whether an unknown Boolean function f : {0, 1}n → {0, 1} is unate (i.e. every variable of f is either non-decreasing or non-incre...Show More

Abstract:

We give an adaptive algorithm that tests whether an unknown Boolean function f : {0, 1}n → {0, 1} is unate (i.e. every variable of f is either non-decreasing or non-increasing) or ε-far from unate with one-sided error and Õ(n3/42) many queries. This improves on the best adaptive O(n/ϵ)-query algorithm from Baleshzar, Chakrabarty, Pallavoor, Raskhodnikova and Seshadhri [1] when 1/ϵ <;<; 4 n1/4. Combined with the Ω̃(n)query lower bound for non-adaptive algorithms with one-sided error of [2], [3], we conclude that adaptivity helps for the testing of unateness with one-sided error. A crucial component of our algorithm is a new subroutine for finding bi-chromatic edges in the Boolean hypercube called adaptive edge search.
Date of Conference: 15-17 October 2017
Date Added to IEEE Xplore: 13 November 2017
ISBN Information:
Print ISSN: 0272-5428
Conference Location: Berkeley, CA, USA

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