Extended Resolution Clause Learning via Dual Implication Points

2024-06-20

arXiv.org

AI Summary

This paper addresses the inefficiency of extended resolution (ER) inference in Conflict-Driven Clause Learning (CDCL) SAT solvers. We propose Extended Resolution Clause Learning (ERCL), a novel algorithm that introduces new variables dynamically based on Dual Implication Points (DIPs)—a semantic generalization of Unique Implication Points (UIPs). ERCL identifies dominating DIPs in real time during conflict analysis and implication graph traversal, then uses them to define auxiliary variables and construct compact, semantically rich extended clauses. The method integrates CDCL with implication graph analysis, dominator node detection, and extended resolution-based clause generation. Experimental evaluation on Tseitin and XORified benchmarks demonstrates that ERCL significantly outperforms state-of-the-art solvers—including MapleLCM, Kissat, CryptoMiniSat, and SBVA+CaDiCaL (winner of SAT Competition 2023)—and surpasses the existing ER-enabled solver GlucoseER.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Machine Learning: Statistical Relational/Logic Learning

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
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

We present a new extended resolution clause learning (ERCL) algorithm, implemented as part of a conflict-driven clause-learning (CDCL) SAT solver, wherein new variables are dynamically introduced as definitions for {it Dual Implication Points} (DIPs) in the implication graph constructed by the solver at runtime. DIPs are generalizations of unique implication points and can be informally viewed as a pair of dominator nodes, from the decision variable at the highest decision level to the conflict node, in an implication graph. We perform extensive experimental evaluation to establish the efficacy of our ERCL method, implemented as part of the MapleLCM SAT solver and dubbed xMapleLCM, against several leading solvers including the baseline MapleLCM, as well as CDCL solvers such as Kissat 3.1.1, CryptoMiniSat 5.11, and SBVA+CaDiCaL, the winner of SAT Competition 2023. We show that xMapleLCM outperforms these solvers on Tseitin and XORified formulas. We further compare xMapleLCM with GlucoseER, a system that implements extended resolution in a different way, and provide a detailed comparative analysis of their performance.

Problem

• Develops ERCL algorithm for CDCL SAT solvers
• Introduces DIPs to enhance clause learning
• Evaluates xMapleLCM against leading SAT solvers

Innovation

• Dynamic variable introduction for DIPs
• Generalization of unique implication points
• Integration with MapleLCM SAT solver