Is BPP0 equal to P0^{RP}?

Ascertain whether the class of problems with constant bounded-error randomized communication complexity (BPP0) coincides with the class computable by constant-cost deterministic protocols with oracle access to some problem in RP (P0^{RP}); i.e., prove or refute BPP0 = P0^{RP}.

Background

This longstanding question (originating in prior work) asks if constant bounded-error randomized protocols can always be simulated by constant-cost deterministic protocols with access to one-sided-error randomized oracles. It probes whether bounded randomness can be captured by deterministic computation plus RP oracles.

Resolving this would refine the landscape of constant-cost communication classes and either yield a powerful simulation principle or establish a fundamental separation.