One-Sided Versus Two-Sided Error in Probabilistic Computation
We demonstrate how to use Lautemann’s proof that BPP is in Σ2p to exhibit that BPP is in RPPromiseRP. 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 ⊂-RPRP for instance. We give a relativized world where P = RP ≠ BPP and thus the promise is indeed needed.
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