Derandomizing from random strings

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F10%3A00352483" target="_blank" >RIV/67985840:_____/10:00352483 - isvavai.cz</a>
Result on the web
—
DOI - Digital Object Identifier
—

Result language
angličtina
Original language name
Derandomizing from random strings
Original language description
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 finda 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 $R_K$ has high Kolmogorov complexity. As a partial converse to our claim we show that strings of very high Kolmogorov-complexity when used as advice are not much more useful than randomly chosen strings.
Czech name
—
Czech description
—

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
Proceedings of the 25th Annual IEEE Conference on Computational Complexity, CCC 2010
ISBN
978-0-7695-4060-3
ISSN
—
e-ISSN
—
Number of pages
6
Pages from-to
—
Publisher name
IEEE Computer Society 2010
Place of publication
Los Alamitos
Event location
Cambridge
Event date
Jun 9, 2010
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
000286932700007

Similar results(10)