Settling the query complexity of non-adaptive junta testing
Xi Chen, Rocco A. Servedio, Li-Yang Tan, Erik Waingarten, Jinyu Xie · 2017
We prove that any non-adaptive algorithm that tests whether an unknown Boolean function f: {0, 1}n → {0, 1} is a k-junta or e-far from every k-junta must make [EQUATION](k3/2 /e) many queries for a wide range of parameters k and e. Our result dramatically improves previous lower bounds from [12, 38], and is essentially optimal given Blais's non-adaptive junta tester from [7], which makes [EQUATION](k3/2)/e queries. Combined with the adaptive tester of [8] which makes O(k log k + k/e) queries, our result shows that adaptivity enables polynomial savings in query complexity for junta testing.