Tractable Weighted First-Order Model Counting with Bounded Treewidth Binary Evidence
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911295931940864 |
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| author | Kůla, Václav Kuang, Qipeng Wang, Yuyi Wang, Yuanhong Kuželka, Ondřej |
| author_facet | Kůla, Václav Kuang, Qipeng Wang, Yuyi Wang, Yuanhong Kuželka, Ondřej |
| contents | The Weighted First-Order Model Counting Problem (WFOMC) asks to compute the weighted sum of models of a given first-order logic sentence over a given domain. Conditioning WFOMC on evidence -- fixing the truth values of a set of ground literals -- has been shown impossible in time polynomial in the domain size (unless $\mathsf{\#P \subseteq FP}$) even for fragments of logic that are otherwise tractable for WFOMC without evidence. In this work, we address the barrier by restricting the binary evidence to the case where the underlying Gaifman graph has bounded treewidth. We present a polynomial-time algorithm in the domain size for computing WFOMC for the two-variable fragments $\text{FO}^2$ and $\text{C}^2$ conditioned on such binary evidence. Furthermore, we show the applicability of our algorithm in combinatorial problems by solving the stable seating arrangement problem on bounded-treewidth graphs of bounded degree, which was an open problem. We also conducted experiments to show the scalability of our algorithm compared to the existing model counting solvers. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_09174 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tractable Weighted First-Order Model Counting with Bounded Treewidth Binary Evidence Kůla, Václav Kuang, Qipeng Wang, Yuyi Wang, Yuanhong Kuželka, Ondřej Logic in Computer Science Artificial Intelligence 03C13, 68T27, 05-08 F.4.0 The Weighted First-Order Model Counting Problem (WFOMC) asks to compute the weighted sum of models of a given first-order logic sentence over a given domain. Conditioning WFOMC on evidence -- fixing the truth values of a set of ground literals -- has been shown impossible in time polynomial in the domain size (unless $\mathsf{\#P \subseteq FP}$) even for fragments of logic that are otherwise tractable for WFOMC without evidence. In this work, we address the barrier by restricting the binary evidence to the case where the underlying Gaifman graph has bounded treewidth. We present a polynomial-time algorithm in the domain size for computing WFOMC for the two-variable fragments $\text{FO}^2$ and $\text{C}^2$ conditioned on such binary evidence. Furthermore, we show the applicability of our algorithm in combinatorial problems by solving the stable seating arrangement problem on bounded-treewidth graphs of bounded degree, which was an open problem. We also conducted experiments to show the scalability of our algorithm compared to the existing model counting solvers. |
| title | Tractable Weighted First-Order Model Counting with Bounded Treewidth Binary Evidence |
| topic | Logic in Computer Science Artificial Intelligence 03C13, 68T27, 05-08 F.4.0 |
| url | https://arxiv.org/abs/2511.09174 |