Stronger LOCAL model preserving Marks’ obstruction

Construct a stronger variant of the LOCAL model in which all efficiently Borel-solvable LCL problems remain efficiently solvable, while 3-coloring acyclic graphs of maximum degree 3 remains impossible by Marks’ method.

Background

The paper seeks a finite-model analogue of the greater visibility available in the Borel setting, while retaining a nontrivial obstruction to 3-coloring.

References

Is there a stronger variant of the LOCAL model (e.g., for which all the LCL problems that are known to admit a Borel solution are efficiently solvable, see ) so that $3$-coloring of acyclic graphs of degree at most $3$ is still not possible, because of Marks' method?

— From descriptive to distributed  (2502.15347 - Grebík et al., 21 Feb 2025) in Problem 15, Section 7 (Generalizations)