Adaptivity Helps for Testing Juntas

Abstract

We give a new lower bound on the query complexity of any non-adaptive algorithm for testing whether an unknown Boolean function is a k-junta versus e-far from every k-junta. Our lower bound is that any non-adaptive algorithm must make [EQUATION] queries for this testing problem, where c is any absolute constant < 1. For suitable values of e this is asymptotically larger than the O(k log k + k/e) query complexity of the best known adaptive algorithm [9] for testing juntas, and thus the new lower bound shows that adaptive algorithms are more powerful than non-adaptive algorithms for the junta testing problem.