Efficient Incremental #SAT via Cross-Instance Knowledge Reuse

2026-05-01

AI Summary

This work proposes an efficient incremental model counting method for sequences of structurally similar Boolean formulas. By introducing a persistent component caching mechanism, the approach reuses results from previously solved subproblems across multiple invocations, thereby avoiding redundant search. Additionally, it incorporates a branching heuristic specifically designed for incremental scenarios to further enhance solving efficiency. This study presents the first integration of structure-aware cross-instance knowledge reuse into a #SAT solving framework, substantially reducing repeated computations. Experimental results demonstrate significant performance improvements over existing model counters in dynamic settings such as argumentation and soft-core reasoning, confirming the effectiveness of leveraging structural similarity in incremental model counting.

Abstract

Model counting ($\#\text{SAT}$) is a fundamental yet $\#\text{P}$-complete problem central to probabilistic reasoning. In this work, we address \textit{incremental model counting}, where sequences of structurally similar formulas must be counted. We propose an approach that amortizes computation via a persistent caching mechanism, retaining component data across solver calls to avoid redundant search. Additionally, we investigate branching heuristics adapted for this setting. We focus on the problems of argumentation and soft core, for which incremental model counting is natural. Experiments demonstrate that our method improves performance compared to current model counters, highlighting the capability of structure-aware reuse in dynamic environments.

Problem

• incremental model counting
• #SAT
• structure reuse
• probabilistic reasoning
• dynamic environments

Innovation

• incremental #SAT
• cross-instance knowledge reuse
• persistent caching
• branching heuristics
• structure-aware reuse