The Lovász local lemma (LLL) is a probabilistic tool to generate combinatorial structures with good “local” properties. The “LLL‐distribution” further shows that these structures have good global properties in expectation. The seminal algorithm of Moser and Tardos turned the simplest, variable‐based form of the LLL into an efficient algorithm; this has since been extended to other probability spaces including random permutations. One can similarly define an “MT‐distribution” for these algorithms, that is, the distribution of the configuration they produce. We show new bounds on the MT‐distribution in the variable and permutation settings which are significantly stronger than those known to hold for the LLL‐distribution. As some example illustrations, we show a nearly tight bound on the minimum implicate size of a CNF Boolean formula, and we obtain improved bounds on weighted Latin transversals and partial Latin transversals.

中文翻译：

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Moser-Tardos发行版的新界限

Lovász局部引理（LLL）是一种概率工具，可生成具有良好“局部”特性的组合结构。“ LLL分布”进一步表明，这些结构具有预期的良好全局特性。Moser和Tardos的开创性算法将最简单的基于变量的LLL形式转化为一种有效的算法。此后已扩展到其他概率空间，包括随机排列。可以类似地为这些算法定义“ MT分布”，即它们产生的配置的分布。我们在变量和置换设置中显示了MT分布的新界限，该界限明显强于LLL分布的已知界限。作为一些示例说明，我们在CNF布尔公式的最小隐含大小上显示了几乎紧密的界限，