The Community for Technology Leaders
2013 IEEE 54th Annual Symposium on Foundations of Computer Science (2002)
Vancouver, BC, Canada
Nov. 16, 2002 to Nov. 19, 2002
ISSN: 0272-5428
ISBN: 0-7695-1822-2
pp: 669
Detlef Ronneburger , Rutgers University
Harry Buhrman , CWI and University of Amsterdam
Michal Koucký , Rutgers University
Dieter van Melkebeek , University of Wisconsin
Eric Allender , Rutgers University
ABSTRACT
<p>We show that sets consisting of strings of high Kolmogorov complexity provide examples of sets that are complete for several complexity classes under probabilistic and non-uniform reductions. These sets are provably not complete under the usual many-one reductions.</p> <p>Let R<sub>K</sub>; R<sub>Kt</sub>; RK<sub>S</sub>;R<sub>KT</sub> be the sets of strings x having complexity at least {{\left| x \right|} \mathord{\left/ {\vphantom {{\left| x \right|} 2}} \right. \kern-\nulldelimiterspace} 2}, according to the usual Kolmogorov complexity measure K, Levin?s time-bounded Kolmogorov complexity Kt [27], a space-bounded Kolmogorov measure KS, and the time-bounded Kolmogorov complexity measure KT that was introduced in [4], respectively.</p> <p>Our main results are: <li>1. R<sub>KS</sub> and R<sub>Kt</sub> are complete for PSPACE and EXP, respectively, under P/poly-truth-table reductions.</li> <li>2. EXP = NP<sup>R<sub>Kt</sub></sup>.</li> <li>3. PSPACE = ZPP^{R_{ks} } \subseteq P^{R_k }.</li> <li>4. The Discrete Log, Factoring, and several lattice problems are solvable in BPP<sup>R<sub>KT</sub></sup>.</li></p>
INDEX TERMS
null
CITATION
Detlef Ronneburger, Harry Buhrman, Michal Koucký, Dieter van Melkebeek, Eric Allender, "Power from Random Strings", 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, vol. 00, no. , pp. 669, 2002, doi:10.1109/SFCS.2002.1181992
82 ms
(Ver 3.3 (11022016))