Testing Juntas

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 ˜O(k2 )/ 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 ˜O(k3/2 )/ 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 ` ˜Ω(k/ ), 2k /k ´ , essentially improving on the previous best lower bound of Ω(k).

• Type: Conference
• Year: 2002
• Where: FOCS
• Authors: Eldar Fischer, Guy Kindler, Dana Ron, Shmuel Safra, Alex Samorodnitsky
• Keywords: FOCS 2002, Lower Bound, Non-adaptive Algorithms, Non-adaptive Testing Algorithms, Theoretical Computer Science