Abstract We define and evaluate a new preprocessing technique for propositional model counting. This technique leverages definability, i.e., the ability to determine that some gates are implied by the input formula Σ. Such gates can be exploited to simplify Σ without modifying its number of models. Unlike previous techniques based on gate detection and replacement, gates do not need to be made explicit in our approach. Our preprocessing technique thus consists of two phases: computing a bipartition 〈 I , O 〉 of the variables of Σ where the variables from O are defined in Σ in terms of I, then eliminating some variables of O in Σ. Our experiments show the computational benefits which can be achieved by taking advantage of our preprocessing technique for model counting.

中文翻译：

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模型计数的可定义性

摘要 我们定义并评估了一种新的命题模型计数预处理技术。该技术利用了可定义性，即确定输入公式 Σ 隐含某些门的能力。可以利用此类门来简化 Σ，而无需修改其模型数量。与以前基于门检测和替换的技术不同，在我们的方法中不需要明确门。因此，我们的预处理技术由两个阶段组成：计算 Σ 变量的二分 < I , O >，其中来自 O 的变量根据 I 定义在 Σ 中，然后消除 Σ 中 O 的一些变量。我们的实验显示了通过利用我们的模型计数预处理技术可以实现的计算优势。