Santha-Vazirani sources, deterministic condensers and very strong extractors
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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An algebraic source is a random variable distributed uniformly over the set of common zeros of one or more multivariate polynomials defined over a finite field F. Our main result is the construction of an explicit deterministic extractor for algebraic sources over exponentially large prime fields. More precisely, we give an explicit (and arguably simple) function E : Fn 7→ {0, 1}m such that the...
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We propose a new model of a weakly random source that admits randomness extraction. Our model of additive sources includes such natural sources as uniform distributions on arithmetic progressions (APs), generalized arithmetic progressions (GAPs), and Bohr sets, each of which generalizes affine sources. We give an explicit extractor for additive sources with linear minentropy over both Zp and Z ...
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We give new constructions of randomness extractors and lossless condensers that are optimal to within constant factors in both the seed length and the output length. For extractors, this matches the parameters of the current best known construction [LRVW03], with an improvement in case the error parameter is small (e.g. 1/poly(n)). For lossless condensers, the previous best constructions achiev...
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ژورنال
عنوان ژورنال: Theory of Computing Systems
سال: 2020
ISSN: 1432-4350,1433-0490
DOI: 10.1007/s00224-020-09975-8