TY - JOUR

T1 - Simple constructions of almost k-wise independent random variables

AU - Alon, Noga

AU - Goldreich, Oded

AU - Hastad, Johan

AU - Peralta, Rene

PY - 1990

Y1 - 1990

N2 - The authors 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 O(log log n + k + log 1/ε), where ε is the statistical difference between the distribution induced on any k-bit locations and the uniform distribution. This is asymptotically comparable to the construction recently presented by J. Naor and M. Naor (1990). An advantage of the present constructions is their simplicity. Two of the constructions are based on bit sequences that are widely believed to possess randomness properties, and the results can be viewed as an explanation and establishment of these beliefs.

AB - The authors 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 O(log log n + k + log 1/ε), where ε is the statistical difference between the distribution induced on any k-bit locations and the uniform distribution. This is asymptotically comparable to the construction recently presented by J. Naor and M. Naor (1990). An advantage of the present constructions is their simplicity. Two of the constructions are based on bit sequences that are widely believed to possess randomness properties, and the results can be viewed as an explanation and establishment of these beliefs.

UR - http://www.scopus.com/inward/record.url?scp=0025535378&partnerID=8YFLogxK

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AN - SCOPUS:0025535378

SN - 0272-5428

VL - 2

SP - 544

EP - 553

JO - Annual Symposium on Foundations of Computer Science - Proceedings

JF - Annual Symposium on Foundations of Computer Science - Proceedings

T2 - Proceedings of the 31st Annual Symposium on Foundations of Computer Science

Y2 - 22 October 1990 through 24 October 1990

ER -