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Dispersers, Deterministic Amplification, and Weak Random Sources. (1989)
| Citations: | 89 - 9 self |
BibTeX
@MISC{Cohen89dispersers,deterministic,
author = {Aviad Cohen and Avi Wigderson},
title = {Dispersers, Deterministic Amplification, and Weak Random Sources.},
year = {1989}
}
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Abstract
We use a certain type of expanding bipartite graphs, called disperser graphs, to design procedures for picking highly correlated samples from a finite set, with the property that the probability of hitting any sufficiently large subset is high. These procedures require a relatively small number of random bits and are robust with respect to the quality of the random bits. Using these sampling procedures to sample random inputs of polynomial time probabilistic algorithms, we can simulate the performance of some probabilistic algorithms with less random bits or with low quality random bits. We obtain the following results: 1. The error probability of an RP or BPP algorithm that operates with a constant error bound and requires n random bits, can be made exponentially small (i.e. 2 \Gamman ), with only (3 + ffl)n random bits, as opposed to standard amplification techniques that require \Omega\Gamma n 2 ) random bits for the same task. This result is nearly optimal, since the informati...
Keyphrases
random bit weak random source deterministic amplification disperser graph omega gamma error probability certain type finite set amplification technique polynomial time probabilistic algorithm large subset constant error bound following result low quality random bit probabilistic algorithm small number bipartite graph random input
