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Summary: What Can be Efficiently Reduced to the
Kolmogorov-Random Strings?
Eric Allender
Rutgers University, New Brunswick, NJ, USA
allender@cs.rutgers.edu
Harry Buhrman
CWI and University of Amsterdam, Amsterdam, Netherlands
buhrman@cwi.nl
Michal Kouck´y
McGill University, Montr´eal, PQ, Canada
mkoucky@cs.mcgill.ca
August 24, 2004
Abstract
We investigate the question of whether one can characterize complexity classes
(such as PSPACE or NEXP) in terms of efficient reducibility to the set of Kolmogorov-
random strings RC. This question arises because PSPACE PRC
and NEXP
NPRC
, and no larger complexity classes are known to be reducible to RC in this
way. We show that this question cannot be posed without explicitly dealing with
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