One-Sided Versus Two-Sided Error in Probabilistic Computation

  • Harry Buhrman
  • Lance Fortnow
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1563)


We demonstrate how to use Lautemann’s proof that BPP is in Σ2 p to exhibit that BPP is in RP PromiseRP . Immediate consequences show that if PromiseRP is easy or if there exist quick hitting set generators then P = BPP. Our proof vastly simplifies the proofs of the later result due to Andreev, Clementi and Rolim and Andreev,

Clementi, Rolim and Trevisan.

Clementi, Rolim and Trevisan question whether the promise is necessary for the above results, i.e., whether BPP ⊂-RP RP for instance. We give a relativized world where P = RP ≠ BPP and thus the promise is indeed needed.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Harry Buhrman
    • 1
  • Lance Fortnow
    • 2
  1. 1.CWIAmsterdamThe Netherlands
  2. 2.Department of Computer ScienceUniversity of ChicagoChicago

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