评估可满足性
Estimating Satisfiability
摘要：
对给定CSP的可满足实例的比例估计问题（约束满足问题）可以通过加权来解决。它包括在每个解决方案上放置一个基于其邻域的非负实值，使得每个可满足实例的总权重至少为1。本文定义了一个一般的加权方案，用于一般CSP的可满足性估计。首先，我们给出加权系统正确的一些充分条件。然后，我们证明了该方案允许将Maneva和Sinclair（2008）获得的3-SAT中非平凡核存在性的上界改进为4.419。另一种更常见的估计可满足性的方法是排序。这包括在域上放置一个全序，它以一种防止回路出现的方式在相邻解之间引入一个方向，然后只计算最小的元素。我们比较了各种条件下的排序和加权。
英文摘要：
The problem of estimating the proportion of satisfiable instances of a given CSP (constraint satisfaction problem) can be tackled through weighting. It consists in putting onto each solution a non-negative real value based on its neighborhood in a way that the total weight is at least 1 for each satisfiable instance. We define in this paper a general weighting scheme for the estimation of satisfiability of general CSPs. First we give some sufficient conditions for a weighting system to be correct. Then we show that this scheme allows for an improvement on the upper bound on the existence of non-trivial cores in 3-SAT obtained by Maneva and Sinclair (2008) to 4.419. Another more common way of estimating satisfiability is ordering. This consists in putting a total order on the domain, which induces an orientation between neighboring solutions in a way that prevents circuits from appearing, and then counting only minimal elements. We compare ordering and weighting under various conditions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
