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An Optimal Tester for k-Linear
[article]

2020
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arXiv
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pre-print

A Boolean function f:{0,1}^n→{0,1} is k-linear if it returns the sum (over the binary field F_2) of k coordinates of the input. In this paper, we study property testing of the classes k-Linear, the class of all k-linear functions, and k-Linear^*, the class ∪_j=0^kj-Linear. We give a non-adaptive distribution-free two-sided ϵ-tester for k-Linear that makes O(klog k+1/ϵ) queries. This matches the lower bound known from the literature. We then give a non-adaptive distribution-free one-sided

arXiv:2006.04409v1
fatcat:3ola32j5m5bvbgcoczikhq6zg4