One-sided vs. two-sided error in constant-cost randomized communication

Determine the relationship between one-sided-error and two-sided-error public-coin randomized protocols in the constant-cost regime; specifically, ascertain whether the class of communication problems computable with constant-cost one-sided-error protocols coincides with (or is strictly weaker than) the class of problems computable with constant-cost two-sided-error protocols.

Background

The paper studies the class BPP of communication problems solvable with constant-cost public-coin randomized protocols. While the authors resolve the existence of a complete problem (showing none exists), they note that key questions about error models remain unresolved even under this constant-cost restriction. Clarifying the power of one-sided versus two-sided error in this regime would sharpen our understanding of how randomness is used most efficiently in communication protocols.