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View all- Ivanov PPavlovic LViola E(2023)On Correlation Bounds against PolynomialsProceedings of the conference on Proceedings of the 38th Computational Complexity Conference10.4230/LIPIcs.CCC.2023.3(1-35)Online publication date: 17-Jul-2023
Bounded Independence versus Symmetric Tests
Article No.: 21, Pages 1 - 27
Abstract
For a test T ⊆ {0, 1}n, define k*(T) to be the maximum k such that there exists a k-wise uniform distribution over {0, 1}n whose support is a subset of T.
For Ht = {x ∈ {0, 1}n : | ∑ixi − n/2| ≤ t}, we prove k*(Ht) = Θ (t2/n + 1).
For Sm, c = {x ∈ {0, 1}n : ∑ixi ≡ c (mod m)}, we prove that k*(Sm, c) = Θ (n/m2). For some k = O(n/m) we also show that any k-wise uniform distribution puts probability mass at most 1/m + 1/100 over Sm, c. Finally, for any fixed odd m we show that there is an integer k = (1 − Ω(1))n such that any k-wise uniform distribution lands in T with probability exponentially close to |Sm, c|/2n; and this result is false for any even m.
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Index Terms
- Bounded Independence versus Symmetric Tests
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December 2019
252 pages
ISSN:1942-3454
EISSN:1942-3462
DOI:10.1145/3331049
- Editor:
- Venkatesan Guruswami
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Publication History
Published: 11 July 2019
Accepted: 01 April 2019
Revised: 01 January 2019
Received: 01 May 2018
Published in TOCT Volume 11, Issue 4
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View all- Ivanov PPavlovic LViola E(2023)On Correlation Bounds against PolynomialsProceedings of the conference on Proceedings of the 38th Computational Complexity Conference10.4230/LIPIcs.CCC.2023.3(1-35)Online publication date: 17-Jul-2023
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