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On Construction of kwise Independent Random Variables
, 1994
"... A 01 probability space is a probability space(\Omega ; 2\Omega ; P ), where the sample space\Omega ` f0; 1g n for some n. A probability space is kwise independent if, when Y i is defined to be the ith coordinate of the random nvector, then any subset of k of the Y i 's is (mutually) in ..."
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Cited by 23 (1 self)
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A 01 probability space is a probability space(\Omega ; 2\Omega ; P ), where the sample space\Omega ` f0; 1g n for some n. A probability space is kwise independent if, when Y i is defined to be the ith coordinate of the random nvector, then any subset of k of the Y i 's is (mutually
Simple Constructions of Almost kwise Independent Random Variables
, 1992
"... We present three alternative simple constructions of small probability spaces on n bits for which any k bits are almost independent. The number of bits used to specify a point in the sample space is (2 + o(1))(log log n + k/2 + log k + log 1 ɛ), where ɛ is the statistical difference between the dist ..."
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Cited by 319 (42 self)
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We present three alternative simple constructions of small probability spaces on n bits for which any k bits are almost independent. The number of bits used to specify a point in the sample space is (2 + o(1))(log log n + k/2 + log k + log 1 ɛ), where ɛ is the statistical difference between
Testing kwise and almost kwise independence
 In 39th Annual ACM Symposium on Theory of Computing
, 2007
"... In this work, we consider the problems of testing whether a distribution over {0, 1} n is kwise (resp. (ɛ, k)wise) independent using samples drawn from that distribution. For the problem of distinguishing kwise independent distributions from those that are δfar from kwise independence in statis ..."
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Cited by 30 (10 self)
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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 (ɛ, k)wise independent distributions from those that are δfar from (ɛ, k)wise independence
Almost kwise vs. kwise independent . . .
, 2013
"... A family of permutations in Sn is kwise independent if a uniform permutation chosen from the family maps any sequence of k distinct elements to any sequence of k distinct elements with equal probability. Efficient constructions of kwise independent permutations are known for k = 2 and k = 3 base ..."
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A family of permutations in Sn is kwise independent if a uniform permutation chosen from the family maps any sequence of k distinct elements to any sequence of k distinct elements with equal probability. Efficient constructions of kwise independent permutations are known for k = 2 and k = 3
kwise independent random graphs
 49TH ANNUAL IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS
, 2008
"... We study the kwise independent relaxation of the usual model G(N, p) of random graphs where, as in this model, N labeled vertices are fixed and each edge is drawn with probability p, however, it is only required that the distribution of any subset of k edges is independent. This relaxation can be r ..."
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Cited by 6 (1 self)
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We study the kwise independent relaxation of the usual model G(N, p) of random graphs where, as in this model, N labeled vertices are fixed and each edge is drawn with probability p, however, it is only required that the distribution of any subset of k edges is independent. This relaxation can
Testing kwise
, 2012
"... A probability distribution over {0, 1}n is kwise independent if its restriction to any k coordinates is uniform. More generally, a discrete distribution D over Σ1 × · · · × Σn is called (nonuniform) kwise independent if for any subset of k indices {i1,..., ik} and for any z1 ∈ Σi1,..., zk ∈ Σ ..."
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∈ Σik, PrX∼D[Xi1 · · ·Xik = z1 · · · zk] = PrX∼D[Xi1 = z1] · · ·PrX∼D[Xik = zk]. kwise independent distributions look random “locally ” to an observer of only k coordinates, even though they may be far from random “globally”. Because of this key feature, kwise independent distributions
Derandomized constructions of kwise (almost) independent permutations
 In Proceedings of the 9th Workshop on Randomization and Computation (RANDOM
, 2005
"... Abstract Constructions of kwise almost independent permutations have been receiving a growingamount of attention in recent years. However, unlike the case of kwise independent functions,the size of previously constructed families of such permutations is far from optimal. This paper gives a new met ..."
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Cited by 24 (4 self)
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Abstract Constructions of kwise almost independent permutations have been receiving a growingamount of attention in recent years. However, unlike the case of kwise independent functions,the size of previously constructed families of such permutations is far from optimal. This paper gives a new
RANDOM WALKS WITH kWISE INDEPENDENT INCREMENTS
, 2004
"... ABSTRACT. We construct examples of a random walk with pairwiseindependent steps which is almostsurely bounded, and for any m and k a random walk with kwise independent steps which has no stationary distribution modulo m. 1. ..."
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Cited by 1 (0 self)
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ABSTRACT. We construct examples of a random walk with pairwiseindependent steps which is almostsurely bounded, and for any m and k a random walk with kwise independent steps which has no stationary distribution modulo m. 1.
On kwise independent distributions and Boolean functions
"... We pursue a systematic study of the following problem. Let f: {0, 1} n → {0, 1} be a (usually monotone) boolean function whose behaviour is well understood when the input bits are identically independently distributed. What can be said about the behaviour of the function when the input bits are not ..."
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Cited by 9 (1 self)
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the extremal properties of kwise independent distributions and provide ways of constructing such distributions. These constructions are connected to linear error correcting codes. We also utilize duality theory and show that for the function f to behave (almost) the same under all kwise independent inputs
Results 1  10
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