Solving Combinatorial Counting Problems with Weighted First-Order Model Counting
The paper presents a new approach to solving combinatorial counting problems using a language called Cofola. This language incorporates first-order logic to address various counting tasks in a structured manner. The authors demonstrate that Cofola can effectively simplify complex counting problems through a systematic compilation process.
- ▪Cofola is a typed declarative language designed for combinatorial counting problems.
- ▪The language includes primitives for common combinatorial objects and applies natural relational and arithmetic constraints.
- ▪A three-phase compilation pipeline transforms problems into weighted first-order model counting instances.
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Computer Science > Artificial Intelligence arXiv:2605.24845 (cs) [Submitted on 24 May 2026] Title:Solving Combinatorial Counting Problems with Weighted First-Order Model Counting Authors:Yuanhong Wang, Juhua Pu, Yuxu Zhou, Yuyi Wang, Ondřej Kuželka View a PDF of the paper titled Solving Combinatorial Counting Problems with Weighted First-Order Model Counting, by Yuanhong Wang and 4 other authors View PDF HTML (experimental) Abstract:Combinatorial counting problems pervade artificial intelligence, statistics, and discrete mathematics. Whether the task is enumerating subsets, multisets, permutations, partitions, or compositions under structural and arithmetic constraints, solving it remains a stubbornly manual exercise.
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