Extending CDCL-based Model Enumeration with Weights
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917470633197568 |
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| author | Spallitta, Giuseppe Vardi, Moshe Y. |
| author_facet | Spallitta, Giuseppe Vardi, Moshe Y. |
| contents | In this work we investigate Weighted Model Enumeration (WME): given a Boolean formula and a weight function over its satisfying assignments, enumerate models while accounting for their weights. This setting supports weight-driven queries, such as producing the top-k models or all models above a threshold. While related to AllSAT, Weighted Model Counting, and MaxSAT, these paradigms do not treat selective enumeration under weights as a native solver task. We present CDCL-based algorithms for WME that integrate weight propagation, weight-based pruning, and weight-aware conflict analysis into both chronological and non-chronological backtracking frameworks. Chronological backtracking exploits implicit blocking and keeps the clause database compact, thereby reducing memory footprint and enabling efficient propagation. In contrast, non-chronological backtracking with clause learning supports explicit blocking and restarts. We show that both approaches are feasible and complementary, highlighting trade-offs in pruning effectiveness with weights and clarifying when each performs best. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_10236 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Extending CDCL-based Model Enumeration with Weights Spallitta, Giuseppe Vardi, Moshe Y. Logic in Computer Science In this work we investigate Weighted Model Enumeration (WME): given a Boolean formula and a weight function over its satisfying assignments, enumerate models while accounting for their weights. This setting supports weight-driven queries, such as producing the top-k models or all models above a threshold. While related to AllSAT, Weighted Model Counting, and MaxSAT, these paradigms do not treat selective enumeration under weights as a native solver task. We present CDCL-based algorithms for WME that integrate weight propagation, weight-based pruning, and weight-aware conflict analysis into both chronological and non-chronological backtracking frameworks. Chronological backtracking exploits implicit blocking and keeps the clause database compact, thereby reducing memory footprint and enabling efficient propagation. In contrast, non-chronological backtracking with clause learning supports explicit blocking and restarts. We show that both approaches are feasible and complementary, highlighting trade-offs in pruning effectiveness with weights and clarifying when each performs best. |
| title | Extending CDCL-based Model Enumeration with Weights |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2603.10236 |