منابع مشابه
Deterministic Extractors for Algebraic Sources
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...
متن کاملExtractors for Turing-Machine Sources
We obtain the first deterministic randomness extractors for n-bit sources with minentropy ≥ n1−α generated (or sampled) by single-tape Turing machines running in time n2−16α, for all sufficiently small α > 0. We also show that such machines cannot sample a uniform n-bit input to the Inner Product function together with the output. The proofs combine a variant of the crossing-sequence technique ...
متن کاملDeterministic Extractors for Additive Sources
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 ...
متن کاملNew Extractors for Interleaved Sources
We study how to extract randomness from a C-interleaved source, that is, a source comprised of C independent sources whose bits or symbols are interleaved. We describe a simple approach for constructing such extractors that yields: • For some δ > 0, c > 0, explicit extractors for 2-interleaved sources on {0, 1} when one source has min-entropy at least (1 − δ)n and the other has min-entropy at l...
متن کاملExtractors for Three Uneven-Length Sources
We construct an efficient 3-source extractor that requires one of the sources to be significantly shorter than the min-entropy of the other two sources. Our extractors work even when the longer, n-bit sources have min-entropy n and the shorter source has min-entropy log n. Previous constructions for independent sources with min-entropy n required Θ(1/γ) sources [Rao06]. Our construction relies ...
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 2014
ISSN: 0097-5397,1095-7111
DOI: 10.1137/11085983x