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Abstract: We show that modified versions of the linear congruential generator and the shift register generator are provably good for amplifying the correctness of a probabilistic algorithm. More precisely, if r random bits are needed for a BPP algorithm to be correct with probability at least 2=3, then O(r + k 2 ) bits are needed to improve this probability to 1 \Gamma 2 \Gammak . We also present a different pseudo-random generator that is optimal, up to a constant factor, in this regard: it uses... (Update)
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BibTeX entry: (Update)
Impagliazzo, R. and D. Zuckerman, "How to Recycle Random Bits", Proceedings of 30th IEEE Symposium on the Foundations of Computer Science, Research Triangle Park, NC, October 1989, pp. 248 -- 253. http://citeseer.ist.psu.edu/impagliazzo89how.html More
@inproceedings{ impagliazzo89how,
author = "Russell Impagliazzo and David Zuckerman",
title = "How to Recycle Random Bits",
booktitle = "{IEEE} Symposium on Foundations of Computer Science",
pages = "248-253",
year = "1989",
url = "citeseer.ist.psu.edu/impagliazzo89how.html" }
Citations (may not include all citations):1447 A Mathematical Theory of Communication (context) - Shannon - 1948 ACM
339 Theory and Applications of Trapdoor Functions (context) - Yao - 1982
334 How to Generate Cryptographically Strong Sequences of Pseudo.. (context) - Blum, Micali - 1984 ACM DBLP
167 Pseudorandom generation from one-way functions (context) - Impagliazzo, Levin et al. - 1989
145 Random Generation of Combinatorial Structures from a Uniform.. (context) - Jerrum, Valiant et al. - 1986 DBLP
139 Ten Lectures on the Probabilistic Method (context) - Spencer - 1987
88 Deterministic Simulation of Logspace (context) - Ajtai, Komlos et al. - 1987
78 Probabilistic algorithm for testing primality (context) - Rabin - 1980
71 Explicit Construction of Linear-Sized Superconcentrators (context) - Gabber, Galil - 1979
40 Explicit Expanders and the Ramanujan conjecture (context) - Lubotzky, Phillips et al. - 1986
36 Universal Hash Functions (context) - Carter, Wegman - 1979
20 Efficiency Considerations in Using Semi-Random Sources (context) - Vazirani - 1987 ACM
18 Realistic Analysis of Some Randomized Algorithms (context) - Bach - 1987 ACM DBLP
18 Dispersers, Deterministic Amplification, and Weak Random Sou.. - Cohen, Wigderson - 1989
14 Inferring a Sequence Generated by a Linear Congruence (context) - Plumstead - 1983 DBLP
12 Randomized Algorithms and Pseudorandom Numbers (context) - Karloff, Raghavan - 1988
9 Randomness, Adversaries and Computation (context) - Vazirani - 1986
6 Expanders, Randomness, or Time versus Space (context) - Sipser - 1986 ACM DBLP
5 Linear Congruential Generators Do Not Produce Random Sequenc.. (context) - Frieze, Kannan et al. - 1984 DBLP
4 On Using Deterministic Functions to Reduce Randomness in Pro.. (context) - Santha ACM DBLP
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