Borel version of the Local Lemma

2016/05/16 by Endre Csóka, Łukasz Grabowski, Csóka, Endre +7 · 1 citation
Mathematics · Computer Science · #Advanced Topology and Set Theory #Mathematical Dynamics and Fractals #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1605.04877

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.

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• Continuous Combinatorics of Abelian Group Actions

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