Derandomizing from Random Strings
Computational Complexity
2009-12-17 v1
Abstract
In this paper we show that BPP is truth-table reducible to the set of Kolmogorov random strings R_K. It was previously known that PSPACE, and hence BPP is Turing-reducible to R_K. The earlier proof relied on the adaptivity of the Turing-reduction to find a Kolmogorov-random string of polynomial length using the set R_K as oracle. Our new non-adaptive result relies on a new fundamental fact about the set R_K, namely each initial segment of the characteristic sequence of R_K is not compressible by recursive means. As a partial converse to our claim we show that strings of high Kolmogorov-complexity when used as advice are not much more useful than randomly chosen strings.
Cite
@article{arxiv.0912.3162,
title = {Derandomizing from Random Strings},
author = {Harry Buhrman and Lance Fortnow and Michal Koucký and Bruno Loff},
journal= {arXiv preprint arXiv:0912.3162},
year = {2009}
}