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Reductions to the Set of Random Strings: The Resource-Bounded Case

  • Eric Allender
  • Harry Buhrman
  • Luke Friedman
  • Bruno Loff
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7464)

Abstract

This paper is motivated by a conjecture [1,5] 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 [5] 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.

Keywords

Turing Machine Random Oracle Winning Strategy Kolmogorov Complexity Random String 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Eric Allender
    • 1
  • Harry Buhrman
    • 2
  • Luke Friedman
    • 1
  • Bruno Loff
    • 3
  1. 1.Department of Computer ScienceRutgers UniversityPiscatawayUSA
  2. 2.CWI and University of AmsterdamThe Netherlands
  3. 3.CWIThe Netherlands

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