Almost Optimal Distribution-free Junta Testing

Abstract

We consider the problem of testing whether an unknown n-variable Boolean function is a k-junta in the distribution-free property testing model, where the distance between functions is measured with respect to an arbitrary and unknown probability distribution over {0, 1} n . Chen, Liu, Servedio, Sheng and Xie [35] showed that the distribution-free k-junta testing can be performed, with one-sided error, by an adaptive algorithm that makes Õ(k 2 )/ǫ queries. In this paper, we give a simple two-sided error adaptive algorithm that makes Õ(k/ǫ) queries.

Quantum Algorithm for Distribution-Free Junta Testing

“…Related Results. During the review phase of this paper, classical complexity of the problem was improved to O(k/ε) queries by Bshouty [4], which is optimal up to logarithmic factors.…”