We do not know yet whether the 2-sided error of $BPP$ allows more computing power than the one sided error of $RP$. In view of derandomization results, the conjectured answer is no, since both classes are conjectured to collapse into $P$. However, not having a proof of that yet, I wonder if there are any results that at least bring $BPP$ closer to $RP$. For example, is there any condition that is known to imply $BPP=RP\cup co-RP$, or $BPP=P^{RP}$, or something similar, but is not known to imply $BPP=RP$?
Narrowing the gap between BPP and RP
complexity classes;randomized algorithms;derandomization