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One-sided-error completeness for BPP

Determine whether every constant-cost randomized communication problem in the class BPP can be computed using a constant number of oracle queries to problems admitting one-sided-error (RP^0) constant-cost protocols.

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Background

The paper surveys the landscape of constant-cost randomized communication (BPP) and notes that all currently known examples can be solved via a constant number of queries to problems in RP0 (one-sided error). Establishing whether this holds universally would significantly clarify the structure of BPP and its relationship to known subclasses.

References

All known problems in BPP can be solved with (1) queries to constant-cost problems with one-sided error (i.e. the class RP0). Is this always true? (See also [HH24]). We mentioned above that finding a complete problem (or hierarchy) could have answered many questions about BPP (depending on the properties of the complete problem itself); these two open problems are examples of that.

— Constant-Cost Communication is not Reducible to k-Hamming Distance (2407.20204 - Fang et al., 29 Jul 2024) in Section: Constant-Cost Communication: the Story so Far and Farther