Abstract
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.
Partially supported by the European Union through NeuroCOLT ESPRIT Working Group Nr. 8556, and HC&M grant nr. ERB4050PL93-0516.
Supported in part by NSF grant CCR 92-53582.
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Buhrman, H., Fortnow, L. (1999). One-Sided Versus Two-Sided Error in Probabilistic Computation. In: Meinel, C., Tison, S. (eds) STACS 99. STACS 1999. Lecture Notes in Computer Science, vol 1563. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49116-3_9
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DOI: https://doi.org/10.1007/3-540-49116-3_9
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