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Almost Optimal Distribution-free Junta Testing

“…In the distribution-free property testing, [28], the distance between Boolean functions is measured with respect to an arbitrary and unknown distribution D over {0, 1} n . In this model, the testing algorithm is allowed (in addition to making black-box queries) to draw random x ∈ {0, 1} n according to the distribution D. This model is studied in [20,23,25,31,35]. For testing k-junta in this model, Chen et al [35] gave a onesided adaptive algorithm that makes Õ(k 2 )/ǫ queries and proved a lower bound Ω(2 k/3 ) for any non-adaptive algorithm.…”

Almost Optimal Testers for Concise Representations

“…In the distribution-free property testing, [38], (and learning [56]) the distance between Boolean functions is measured with respect to an arbitrary and unknown distribution D over {0, 1} n . In the distribution-free model, the testing (and learning) algorithm is allowed (in addition to making black-box queries) to draw random x ∈ {0, 1} n according to the distribution D. This model is studied in [15,27,32,34,41,45].…”

“…In this paper we prove the following result for the distribution-free model. When k = n, better results can be found in [34,32].…”