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STOC
2007
ACM

Testing k-wise and almost k-wise independence

14 years 4 months ago
Testing k-wise and almost k-wise independence
In this work, we consider the problems of testing whether a distribution over {0, 1}n is k-wise (resp. ( , k)-wise) independent using samples drawn from that distribution. For the problem of distinguishing k-wise independent distributions from those that are -far from k-wise independence in statistical distance, we upper bound the number of required samples by ~O(nk /2 ) and lower bound it by (n k-1 2 /) (these bounds hold for constant k, and essentially the same bounds hold for general k). To achieve these bounds, we use Fourier analysis to relate a distribution's distance from k-wise independence to its biases, a measure of the parity imbalance it induces on a set of variables. The relationships we derive are tighter than previously known, and may be of independent interest. To distinguish ( , k)-wise independent distributions from those that are -far from ( , k)-wise independence in statistical distance, we upper bound the number of required samples by O `k log n 2 2 ? and low...
Noga Alon, Alexandr Andoni, Tali Kaufman, Kevin Ma
Added 03 Dec 2009
Updated 03 Dec 2009
Type Conference
Year 2007
Where STOC
Authors Noga Alon, Alexandr Andoni, Tali Kaufman, Kevin Matulef, Ronitt Rubinfeld, Ning Xie
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