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Abstract: This paper provides the first explicit construction of extractors which are simultaneously optimal up to constant factors in both seed length and output length. More precisely, for every n, k, our extractor uses a random seed of length O(log n) to transform any random source on n bits with (min-)entropy k, into a distribution on (1 #)k bits that is #-close to uniform. Here # and # can be taken to be any positive constants. (In fact, # can be almost polynomially small). (Update)
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BibTeX entry: (Update)
C. Lu, O. Reingold, S. Vadhan, and A. Wigderson. Extractors: Optimal Up to Constant Factors. In Proceedings of 35th ACM STOC, 2003. Preliminary version. http://citeseer.ist.psu.edu/lu03extractors.html More
@misc{ lu03extractors,
author = "C. Lu and O. Reingold and S. Vadhan and A. Wigderson",
title = "Extractors: Optimal Up to Constant Factors",
text = "C. Lu, O. Reingold, S. Vadhan, and A. Wigderson. Extractors: Optimal Up
to Constant Factors. In Proceedings of 35th ACM STOC, 2003. Preliminary
version.",
year = "2003",
url = "citeseer.ist.psu.edu/lu03extractors.html" }
Citations (may not include all citations):242 Nondeterministic exponential time has two-prover interactive.. - Babai, Fortnow et al. - 1991
132 Hiding instances in multioracle queries (context) - Beaver, Feigenbaum - 1990
120 Unbiased bits from sources of weak randomness and probabilis.. - Chor, Goldreich - 1988
94 Self testingcorrecting with application to numerical problem - Luby, testing et al. - 1993
90 A pseudorandom generator from any one-way function - Hastad, Impagliazzo et al. - 1999
86 New directions in testing (context) - Lipton - 1989
84 Simulating BPP using a general weak random source - Zuckerman - 1996
75 Randomness is linear in space - Nisan, Zuckerman - 1996
64 Pseudorandom generators without the XOR lemma - Sudan, Trevisan et al. - 2001
61 Expanders that beat the eigenvalue bound: explicit construct.. - Wigderson, Zuckerman - 1999
47 Extracting all the randomness and reducing the error in Trev.. - Raz, Reingold et al. - 2002
40 Tiny families of functions with random properties: A quality.. - Goldreich, Wigderson - 1997
36 Randomness-optimal oblivious sampling - Zuckerman - 1997
36 Extracting randomness: A survey and new constructions - Nisan, Ta-Shma - 1999
21 Extractors and pseudo-random generators with optimal seed le.. - Impagliazzo, Shaltiel et al. - 2000
19 Error reduction for extractors - Raz, Reingold et al.
18 Extracting randomness via repeated condensing - Reingold, Shaltiel et al. - 2000
17 Simple extractors for all min-entropies and a new pseudo-ran.. (context) - Shaltiel, Umans - 2001
16 On extracting randomness from weak random sources (context) - Ta-Shma - 1996
14 A sample of samplers: A computational perspective on samplin.. - Goldreich - 1997
14 and new constant-degree expanders and extractors (context) - Reingold, Vadhan et al. - 2000
13 Exponential lower bounds for 2-query locally decodable codes - de Wolf, Kerenidis - 2003
10 Recent developments in explicit constructions of extractors (context) - Shaltiel - 2002
10 ciency of local decoding procedures for error-correcting cod.. (context) - Katz, Trevisan - 2000
8 Extractors and pseudorandom generators - Trevisan - 2001
7 On constructing locally computable extractors and cryptosyst.. - Vadhan - 2002
7 Extractor codes (context) - Ta-Shma, Zuckerman - 2001
6 Loss-less condensers (context) - Ta-Shma, Umans et al. - 2001
6 Randomness conductors and constant-degree lossless expanders (context) - Capalbo, Reingold et al. - 2002
6 Extractors from Reed--Muller codes (context) - Ta-Shma, Zuckerman et al. - 2001
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