We propose a unifying dynamic-programming framework to compute exact literal-weighted model counts of formulas in conjunctive normal form. At the center of our framework are project-join trees, which specify efficient project-join orders to apply additive projections (variable eliminations) and joins (clause multiplications). In this framework, model counting is performed in two phases. First, the planning phase constructs a project-join tree from a formula. Second, the execution phase computes the model count of the formula, employing dynamic programming as guided by the project-join tree. We empirically evaluate various methods for the planning phase and compare constraint-satisfaction heuristics with tree-decomposition tools. We also investigate the performance of different data structures for the execution phase and compare algebraic decision diagrams with tensors. We show that our dynamic-programming model-counting framework DPMC is competitive with the state-of-the-art exact weighted model counters cachet, c2d, d4, and miniC2D.

中文翻译：

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DPMC：通过动态规划对项目连接树进行加权模型计数

我们提出了一个统一的动态编程框架，以计算合取范式中公式的精确字面加权模型计数。我们框架的中心是项目连接树，它指定有效的项目连接顺序来应用加法投影（变量消除）和连接（子句乘法）。在这个框架中，模型计数分两个阶段进行。首先，计划阶段根据公式构建项目连接树。其次，执行阶段计算公式的模型计数，在项目连接树的指导下采用动态规划。我们凭经验评估规划阶段的各种方法，并将约束满足启发式方法与树分解工具进行比较。我们还研究了不同数据结构在执行阶段的性能，并将代数决策图与张量进行了比较。我们展示了我们的动态编程模型计数框架 DPMC 与最先进的精确加权模型计数器 cachet、c2d、d4 和 miniC2D 具有竞争力。