Computational BPP versus NP and coNP

Determine the corresponding computational comparisons between BPP and NP and between BPP and coNP, which remain unresolved despite the known incomparability of the analogous communication-complexity classes.

Background

The paper contrasts communication complexity with computational complexity. In communication complexity, BPP is known to be incomparable with both NP and coNP, while the authors state that the corresponding comparisons in ordinary computational complexity remain unresolved. This open issue is presented as part of the broader motivation for studying finer relationships among randomized, nondeterministic, and polynomial-hierarchy-like communication classes.

References

In communication complexity, $BPP$ is incomparable with both $NP$ and $\mathsf{coNP}$, whereas the corresponding computational comparisons remain open.

— Efficient Randomized Communication Without Large Monochromatic Rectangles  (2609.20763 - Wang et al., 17 Sep 2026) in Section 1, Introduction