What can be efficiently reduced to the Kolmogorov-random strings?

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 Kolmogorovrandom 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 issues raised by the choice of universal machine in the definition of Kolmogorov complexity. What follows is a list of some of our main results.

• Type: Journal
• Year: 2006
• Where: APAL
• Authors: Eric Allender, Harry Buhrman, Michal Koucký
• Keywords: APAL 2006, Complexity Classes, Nsf Grant Ccr-0104823, Universal Machine