Separating complexity classes of LCL problems on grids

TL;DR

This paper investigates the complexity of locally checkable labeling problems on grid graphs using advanced theoretical frameworks, revealing new distinctions among complexity classes and challenging existing conjectures.

Contribution

It introduces novel separations of complexity classes for LCL problems on grids, providing counterexamples to prior conjectures in the field.

Findings

Different complexity classes for LCL problems are now distinguished.

Counterexamples challenge previous assumptions about LCL problem complexities.

New theoretical tools link descriptive set theory, computability, and graph problems.

Abstract

We study the complexity of locally checkable labeling (LCL) problems on $\mathbb{Z}^n$ from the point of view of descriptive set theory, computability theory, and factors of i.i.d. Our results separate various complexity classes that were not previously known to be distinct and serve as counterexamples to a number of natural conjectures in the field.