What Can be Efficiently Reduced to the Kolmogorov-Random Strings?

@article{Allender2004WhatCB,
  title={What Can be Efficiently Reduced to the Kolmogorov-Random Strings?},
  author={Eric Allender and Harry Buhrman and Michal Kouck{\'y}},
  journal={Ann. Pure Appl. Logic},
  year={2004},
  volume={138},
  pages={2-19}
}
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. 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. Among other results, we show that although for every universal machine U , there are very complex sets that are ≤ dtt -reducible to RCU , it is… CONTINUE READING