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Pseudorandom Generators for Group Products (version with the geometric proof — 2nd draft) (2011)
BibTeX
@MISC{Nimbhorkar11pseudorandomgenerators,
author = {Prajakta Nimbhorkar and Pavel Pudlák},
title = {Pseudorandom Generators for Group Products (version with the geometric proof — 2nd draft)},
year = {2011}
}
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Abstract
We prove that the pseudorandom generator introduced by Impagliazzo et al. in [INW94] with proper choice of parameters fools group products of a given finite group G. The seed length is O(log n(|G | O(1) +log 1 δ)), where n is the length of the word and δ is the allowed error. The result implies that the pseudorandom generator with seed length O(log n(2O(w log w) + log 1 δ)) fools read-once permutation branching programs of width w. As an application of the pseudorandom generator one obtains small-bias spaces for products over all finite groups [MZ09].
