Deterministic Randomness Extraction from Generalized and Distributed Santha--Vazirani Sources
نویسندگان
چکیده
منابع مشابه
Deterministic Randomness Extraction from Generalized and Distributed Santha-Vazirani Sources
A Santha-Vazirani (SV) source is a sequence of random bits where the conditional distribution of each bit, given the previous bits, can be partially controlled by an adversary. Santha and Vazirani show that deterministic randomness extraction from these sources is impossible. In this paper, we study the generalization of SV sources for non-binary sequences. We show that unlike the binary case, ...
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Let F be a finite alphabet and D be a finite set of distributions over F . A Generalized Santha-Vazirani (GSV) source of type (F ,D), introduced by Beigi, Etesami and Gohari (ICALP 2015, SICOMP 2017), is a random sequence (F1, . . . , Fn) in Fn, where Fi is a sample from some distribution d ∈ D whose choice may depend on F1, . . . , Fi−1. We show that all GSV source types (F ,D) fall into one o...
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Given two independent weak random sources X,Y , with the same length l and min-entropies bX , bY whose sum is greater than l + Ω(polylog(l/ε)), we construct a deterministic two-source extractor (aka “blender”) that extracts max(bX , bY ) + (bX + bY − l − 4 log(1/ε)) bits which are ε-close to uniform. In contrast, best previously published construction [4] extracted at most 1 2 (bX + bY − l− 2 l...
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Preface Roughly speaking, a deterministic extractor is a function that 'extracts' almost perfect random bits from a 'weak random source'-a distribution that contains some entropy but is far from being truly random. In this book we explicitly construct deterministic extractors and related objects for various types of sources. A basic theme in this book is a methodology of recycling randomness th...
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 2017
ISSN: 0097-5397,1095-7111
DOI: 10.1137/15m1027206