Testing k-wise and almost k-wise independence

@inproceedings{Alon2007TestingKA,
  title={Testing k-wise and almost k-wise independence},
  author={Noga Alon and Alexandr Andoni and Tali Kaufman and Kevin Matulef and Ronitt Rubinfeld and Ning Xie},
  booktitle={STOC},
  year={2007}
}
In this work, we consider the problems of testing whether adistribution over (0,1<sup>n</sup>) is <i>k</i>-wise (resp. (ε,k)-wise) independentusing samples drawn from that distribution. For the problem of distinguishing <i>k</i>-wise independent distributions from those that are δ-far from <i>k</i>-wise independence in statistical distance, we upper bound the number ofrequired samples by Õ(n<sup>k</sup>/δ<sup>2</sup>) and lower bound it by Ω(n<sup>k-1/2</sup>/δ) (these bounds hold for constant… CONTINUE READING
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