Abstract

We demonstrate how to use Lautemann's proof that BPP is in \Sigma p 2 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 simpliøes 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 6= BPP and thus the promise is indeed needed.

Citations