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

Amir Ben-Dor; Anna Karlin; Nathan Linial; Yuri Rabinovich

doi:10.1006/jcss.1997.1551

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

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

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

An ∈-biased random source is a sequence X= (X₁, X₂,..., X_n) of 0, 1-valued random variables such that the conditional probability Pr[X_i=1|X₁,X₂,..., X_i-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 Pr_x(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 language	English
Pages (from-to)	174-176
Number of pages	3
Journal	Journal of Computer and System Sciences
Volume	58
Issue number	1
DOIs	https://doi.org/10.1006/jcss.1997.1551
State	Published - Feb 1999

Bibliographical note

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

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science
Computer Networks and Communications
Computational Theory and Mathematics
Applied Mathematics

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10.1006/jcss.1997.1551

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title = "A note on the influence of an ∈-biased random source",

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 ∈.",

author = "Amir Ben-Dor and Anna Karlin and Nathan Linial and Yuri Rabinovich",

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AU - Karlin, Anna

AU - Linial, Nathan

AU - Rabinovich, Yuri

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

Abstract

Bibliographical note

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