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The non-adaptive query complexity of testing k-parities

Harry Buhrman
David Garcia
Arie Matsliah
Ronald de Wolf
Chicago Journal of Theoretical Computer Science, vol. 2013 (2013), pp. 1-11


We prove tight bounds of Θ(klogk) queries for non-adaptively testing whether a function f:{0,1}^n→{0,1} is a k-parity or far from any k-parity. The lower bound combines a recent method of Blais, Brody and Matulef to get lower bounds for testing from communication complexity with an Ω(klogk) lower bound for the one-way communication complexity of k-disjointness.