Adaptivity Helps for Testing Juntas
نویسندگان
چکیده
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 ε-far from every k-junta. Our lower bound is that any non-adaptive algorithm must make Ω ( k log k εc log(log(k)/εc) ) queries for this testing problem, where c is any absolute constant < 1. For suitable values of ε this is asymptotically larger than the O(k log k + k/ε) 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. 1998 ACM Subject Classification F.2 Analysis of Algorithms and Problem Complexity
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