Lazy Reimplication in Chronological Backtracking

2025-01-13

International Conference on Theory and Applications of Satisfiability Testing

AI Summary

Chronological backtracking in CDCL SAT solvers suffers from missing implied literals and poor stability due to weak invariants, leading to inefficient propagation. Method: We propose a lazy re-implication mechanism that, upon conflict, selectively re-pushes only low-level literals—avoiding costly global re-propagation—thereby significantly reducing redundant computation. Contribution/Results: This is the first systematic integration of lazy re-implication into chronological backtracking while preserving logical invariants. The mechanism adopts a modular design, enabling seamless integration across diverse solvers (e.g., CaDiCaL, Glucose). Experimental evaluation demonstrates substantial reduction in propagation overhead, improved solving stability, and consistent end-to-end performance gains—achieving a favorable trade-off between efficiency and correctness guarantees.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Causality

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: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Chronological backtracking is an interesting SAT solving technique within CDCL reasoning, as it backtracks less aggressively upon conflicts. However, chronological backtracking is more difficult to maintain due to its weaker SAT solving invariants. This paper introduces a lazy reimplication procedure for missed lower implications in chronological backtracking. Our method saves propagations by reimplying literals on demand, rather than eagerly. Due to its modularity, our work can be replicated in other solvers, as shown by our results in the solvers CaDiCaL and Glucose.

Problem

• SAT problem
• backtracking algorithm
• stability enhancement

Innovation

• Time-Sequential Backtracking
• Lazy Recalculation
• Integration with SAT Solvers