The maximal probability that k-wise independent bits are all 1
نویسندگان
چکیده
منابع مشابه
The maximal probability that k-wise independent bits are all 1
A k-wise independent distribution on n bits is a joint distribution of the bits such that each k of them are independent. In this paper we consider k-wise independent distributions with identical marginals, each bit has probability p to be 1. We address the following question: how high can the probability that all the bits are 1 be, for such a distribution? For a wide range of the parameters n,...
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A probability distribution over {0, 1} is k-wise independent if its restriction to any k coordinates is uniform. More generally, a discrete distribution D over Σ1 × · · · × Σn is called (non-uniform) k-wise independent if for any subset of k indices {i1, . . . , ik} and for any z1 ∈ Σi1 , . . . , zk ∈ Σik , PrX∼D[Xi1 · · ·Xik = z1 · · · zk] = PrX∼D[Xi1 = z1] · · ·PrX∼D[Xik = zk]. k-wise indepen...
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A distribution D over Σ1 × · · · × Σn is called (non-uniform) k-wise independent if for any set of k indices {i1, . . . , ik} and for any z1 · · · zk ∈ Σi1 × · · · × Σik , PrX∼D[Xi1 · · ·Xik = z1 · · · zk] = PrX∼D[Xi1 = z1] · · ·PrX∼D[Xik = zk]. We study the problem of testing (non-uniform) k-wise independent distributions over product spaces. For the uniform case we show an upper bound on the ...
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ژورنال
عنوان ژورنال: Random Structures & Algorithms
سال: 2010
ISSN: 1042-9832
DOI: 10.1002/rsa.20329