Testing juntas nearly optimally

14 years 3 months ago
Testing juntas nearly optimally
A function on n variables is called a k-junta if it depends on at most k of its variables. In this article, we show that it is possible to test whether a function is a k-junta or is "far" from being a k-junta with O(k/ + k log k) queries, where is the approximation parameter. This result improves on the previous best upper bound of ~O(k3/2 )/ queries and is asymptotically optimal, up to a logarithmic factor. We obtain the improved upper bound by introducing a new algorithm with one-sided error for testing juntas. Notably, the algorithm is a valid junta tester under very general conditions: it holds for functions with arbitrary finite domains and ranges, and it holds under any product distribution over the domain. A key component of the analysis of the new algorithm is a new structural result on juntas: roughly, we show that if a function f is "far" from being a k-junta, then f is "far" from being determined by k parts in a random partition of the variable...
Eric Blais
Added 23 Nov 2009
Updated 23 Nov 2009
Type Conference
Year 2009
Where STOC
Authors Eric Blais
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