eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2016-09-06
24:1
24:9
10.4230/LIPIcs.APPROX-RANDOM.2016.24
article
Bounded Independence vs. Moduli
Boppana, Ravi
Håstad, Johan
Lee, Chin Ho
Viola, Emanuele
Let k = k(n) be the largest integer such that there exists a k-wise uniform distribution over {0,1}^n that is supported on the set S_m := {x in {0,1}^n: sum_i x_i equiv 0 mod m}, where m is any integer. We show that Omega(n/m^2 log m) <= k <= 2n/m + 2. For k = O(n/m) we also show that any k-wise uniform distribution puts probability mass at most 1/m + 1/100 over S_m. For any fixed odd m there is k \ge (1 - Omega(1))n such that any k-wise uniform distribution lands in S_m with probability exponentially close to |S_m|/2^n; and this result is false for any even m.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol060-approx-random2016/LIPIcs.APPROX-RANDOM.2016.24/LIPIcs.APPROX-RANDOM.2016.24.pdf
Bounded independence
Modulus