The non-adaptive query complexity of testing k-parities


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.