  We study the position of the computable setting in the "common theory of
locality" developed in arXiv:2106.02066 and arXiv:2204.09329 for local problems
on $\Delta$-regular trees, $\Delta \in \omega$. We show that such a problem
admits a computable solution on every highly computable $\Delta$-regular forest
if and only if it admits a Baire measurable solution on every Borel
$\Delta$-regular forest. We also show that if such a problem admits a
computable solution on every computable maximum degree $\Delta$ forest then it
admits a continuous solution on every maximum degree $\Delta$ Borel graph with
appropriate topological hypotheses, though the converse does not hold.
