Improved Bounds for Testing Juntas
نویسنده
چکیده
We consider the problem of testing functions for the property of being a k-junta (i.e., of depending on at most k variables). Fischer, Kindler, Ron, Safra, and Samorodnitsky (J. Comput. Sys. Sci., 2004 ) showed that Õ(k)/ queries are sufficient to test k-juntas, and conjectured that this bound is optimal for non-adaptive testing algorithms. Our main result is a non-adaptive algorithm for testing k-juntas with Õ(k)/ queries. This algorithm disproves the conjecture of Fischer et al. We also show that the query complexity of non-adaptive algorithms for testing juntas has a lower bound of min Ω̃(k/ ), 2/k , essentially improving on the previous best lower bound of Ω(k).
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تاریخ انتشار 2008