BAIRE versus COMPUTABLE on grids

Determine whether BAIRE(Z^n) is contained in COMPUTABLE(Z^n) for every integer n at least 2.

Background

The paper proves that COMPUTABLE(Zn) is not contained in BAIRE(Zn), thereby separating the two classes in one direction. It explicitly leaves open the reverse inclusion, which would necessarily be strict if true.

References

We do not know whether the opposite inclusion $BAIRE(Zn) \subseteq COMPUTABLE(Zn)$ holds; indeed, it could even be that $BAIRE() \subseteq COMPUTABLE()$ for every finitely generated group $\Gamma$.

— Separating complexity classes of LCL problems on grids  (2501.17445 - Berlow et al., 29 Jan 2025) in Section 1, paragraph following Theorem 1.8