Derandomizing from Random Strings

—In this paper we show that BPP is truth-table reducible to the set of Kolmogorov random strings RK . It was previously known that PSPACE, and hence BPP is Turingreducible to RK . The earlier proof relied on the adaptivity of the Turing-reduction to find a Kolmogorov-random string of polynomial length using the set RK as oracle. Our new nonadaptive result relies on a new fundamental fact about the set RK , namely each initial segment of the characteristic sequence of RK has high Kolmogorov complexity. As a partial converse to our claim we show that strings of very high Kolmogorovcomplexity when used as advice are not much more useful than randomly chosen strings.

• Type: Conference
• Year: 2010
• Where: COCO
• Authors: Harry Buhrman, Lance Fortnow, Michal Koucký, Bruno Loff
• Keywords: Algorithms, COCO 2010, Earlier Proof, Kolmogorov Random Strings, Set Rk