One-sided versus two-sided error in probabilistic computation

We demonstrate how to use Lautemann's proof that BPP is in Sigma(2)(p) 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 subset of or equal to RPRP for instance. We give a relativized world where P = RP not equal BPP and thus the promise is indeed needed.