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Separating complexity classes of LCL problems on grids

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arxiv 2501.17445 v4 pith:X4VDGTBD submitted 2025-01-29 math.LO cs.CCmath.COmath.PR

Katalin Berlow , Anton Bernshteyn , Clark Lyons , Felix Weilacher This is my paper · ORCID
classification math.LOcs.CCmath.COmath.PR
keywords complexityclassesproblemstheorycheckablecomputabilityconjecturescounterexamples
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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.

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  1. New Complexity Classes in Locally Checkable Labeling for Local Computation Algorithms

    cs.DC 2026-07 accept novelty 7.0 of 10

    Stacking of Rosenbaum–Suomela base LCLs yields LCLs of randomized VOLUME/LCA probe complexity Θ(log^k n) and ˜Θ(n^{p/q}) on bounded-degree graphs and trees.

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