Borel version of the Local Lemma
Combinatorics
2024-03-05 v2 Dynamical Systems
Probability
Abstract
We prove a Borel version of the local lemma, i.e. we show that, under suitable assumptions, if the set of variables in the local lemma has a structure of a Borel space, then there exists a satisfying assignment which is a Borel function. The main tool which we develop for the proof, which is of independent interest, is a parallel version of the Moser-Tardos algorithm which uses the same random bits to resample clauses that are far enough in the dependency graph.
Cite
@article{arxiv.1605.04877,
title = {Borel version of the Local Lemma},
author = {Endre Csóka and Łukasz Grabowski and András Máthé and Oleg Pikhurko and Konstantinos Tyros},
journal= {arXiv preprint arXiv:1605.04877},
year = {2024}
}
Comments
26 pages; note that this manuscript is fully superseded by preprint arxiv:2203.05888