Eric Allender ; Harry Buhrman ; Luke Friedman ; Bruno Loff - Reductions to the set of random strings: The resource-bounded case

lmcs:723 - Logical Methods in Computer Science, August 19, 2014, Volume 10, Issue 3 - https://doi.org/10.2168/LMCS-10(3:5)2014
Reductions to the set of random strings: The resource-bounded case

Authors: Eric Allender ; Harry Buhrman ; Luke Friedman ; Bruno Loff

This paper is motivated by a conjecture that BPP can be characterized in terms of polynomial-time nonadaptive reductions to the set of Kolmogorov-random strings. In this paper we show that an approach laid out in [Allender et al] to settle this conjecture cannot succeed without significant alteration, but that it does bear fruit if we consider time-bounded Kolmogorov complexity instead. We show that if a set A is reducible in polynomial time to the set of time-t-bounded Kolmogorov random strings (for all large enough time bounds t), then A is in P/poly, and that if in addition such a reduction exists for any universal Turing machine one uses in the definition of Kolmogorov complexity, then A is in PSPACE.


Volume: Volume 10, Issue 3
Published on: August 19, 2014
Accepted on: June 25, 2015
Submitted on: November 6, 2012
Keywords: Computer Science - Computational Complexity,Computer Science - Logic in Computer Science


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