Rethinking Clause Management for CDCL SAT Solvers

2026-02-24

AI Summary

This work addresses the inefficiency of mainstream CDCL SAT solvers in verifying complex arithmetic circuits—such as multipliers—where overreliance on the LBD (Literal Block Distance) heuristic leads to suboptimal clause management, effectively reducing clause selection to a simplistic length-based criterion that fails to capture dynamic usage patterns. To overcome this limitation, the paper proposes a novel clause reduction mechanism that decouples a learned clause’s intrinsic lineage from its dynamic usage behavior, modeling each aspect independently to assess clause quality more accurately. This approach breaks free from the LBD-centric paradigm and achieves up to a 5.74× speedup on challenging arithmetic circuit verification instances while maintaining performance competitive with state-of-the-art solvers on general benchmarks, thereby significantly enhancing overall solving efficiency.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Search and Optimization: Heuristic Search
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Boolean Satisfiability (SAT) solving underpins a wide range of applications in Electronic Design Automation (EDA), particularly formal verification. However, this paper observes that the mainstream clause reduction heuristic in modern SAT solvers becomes ineffective in the critical domain of complex arithmetic circuit verification, such as multipliers. On these instances, the dominant Literal Block Distance (LBD) metric for measuring clause quality degrades into a simple value of clause length, without any perception of dynamic clause usage during solving.To address this issue, a novel clause reduction mechanism is proposed, which is entirely independent of LBD. Its core idea is to decouple and handle separately the two most fundamental characteristics of learnt clauses--inherent lineage and dynamic usage patterns--thereby avoiding the efficiency degradation caused by inappropriately mixing these properties. Experiments show that our method consistently improves mainstream solvers and achieves speedups of up to 5.74x on complex arithmetic circuit problems, while maintaining comparable performance on general-purpose benchmarks. These results challenge the prevailing LBD-centric clause quality metric for clause management.

Problem

• SAT solving
• clause management
• LBD
• arithmetic circuit verification
• CDCL

Innovation

• clause management
• CDCL SAT solver
• LBD
• arithmetic circuit verification
• learned clause