TY - JOUR
T1 - A note on the influence of an ∈-biased random source
AU - Ben-Dor, Amir
AU - Karlin, Anna
AU - Linial, Nathan
AU - Rabinovich, Yuri
N1 - Funding Information:
* Research supported by the Israel Academy of Science.
PY - 1999/2
Y1 - 1999/2
N2 - 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 ∈.
AB - 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 ∈.
UR - http://www.scopus.com/inward/record.url?scp=0033075134&partnerID=8YFLogxK
U2 - 10.1006/jcss.1997.1551
DO - 10.1006/jcss.1997.1551
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AN - SCOPUS:0033075134
SN - 0022-0000
VL - 58
SP - 174
EP - 176
JO - Journal of Computer and System Sciences
JF - Journal of Computer and System Sciences
IS - 1
ER -