Randomness, relativizations, and polynomial reducibilities

  • Klaus Ambos-Spies
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 223)


We show that, for any set A which cannot be computed in polynomial time, the class of sets p-many-one incomparable with A has measure 1, whereas in case of p-Turing reducibility the class of sets incomparable with A has measure 1 if and only if A is not in the class BPP, the class of problems which can be probabilisticly solved with uniformly bounded error probability in polynomial time. Consequences for the reducibility relation between a randomly chosen pair of problems are discussed. Moreover, it is shown that any class, which in the relativized case collapses to P with probability one, is actually contained in BPP.


Polynomial Time Turing Machine Random Oracle Measurable Classis Minimal Pair 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Klaus Ambos-Spies
    • 1
  1. 1.Lehrstuhl für Informatik IIUniversität DortmundGermany

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