We show that throughout the satisfiable phase the normalized number of satisfying assignments of a random 2‐SAT formula converges in probability to an expression predicted by the cavity method from statistical physics. The proof is based on showing that the Belief Propagation algorithm renders the correct marginal probability that a variable is set to “true” under a uniformly random satisfying assignment.

中文翻译：

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随机2-SAT公式的满意分配数

我们表明，在整个可满足阶段中，随机2-SAT公式的满意赋值的归一化数量会收敛于由腔体方法根据统计物理学预测的表达式。该证明基于表明，在一致随机满足的分配条件下，信念传播算法可提供正确的边际概率，即变量被设置为“真”。