A note on the influence of an ∈-biased random source

Amir Ben-Dor*, Anna Karlin, Nathan Linial, Yuri Rabinovich

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

An ∈-biased random source is a sequence X= (X1, X2,..., Xn) of 0, 1-valued random variables such that the conditional probability Pr[Xi=1|X1,X2,..., Xi-1] is always between 1/2-∈ and 1/2+∈+∈. Given a family S⊆,{o,1 of binary strings of length n, its ∈-enhanced probability Pr(S) is defined as the maximum of Prx(S) over all ∈-biased random sources X In this paper we establish a tight lower bound on Pr(S) as a function of |S|, n and ∈.

Original languageAmerican English
Pages (from-to)174-176
Number of pages3
JournalJournal of Computer and System Sciences
Volume58
Issue number1
DOIs
StatePublished - Feb 1999

Bibliographical note

Funding Information:
* Research supported by the Israel Academy of Science.

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