Lower bounds for reducibility to the Kolmogorov random strings

Authors:
John M. Hitchcock
Affiliations:
Department of Computer Science, University of Wyoming
Venue:
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
Year:
2010

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Abstract

We show the following results for polynomial-time reducibility to RC, the set of Kolmogorov random strings. 1. If P ≠ NP, then SAT does not dtt-reduce to RC. 2. If PH does not collapse, then SAT does not nα-tt-reduce to RC for any α nα-T-reduce to RC for any α RC. 5. There is a problem in E that does not nα-tt-reduce to RC, for any α nα-T-reduce to RC, for any α These results hold for both the plain and prefix-free variants of Kolmogorov complexity and are also independent of the choice of the universal machine.