Generalizing CDCL with Graph Backtracking

2026-05-27

AI Summary

This work addresses a key limitation of traditional conflict-driven clause learning (CDCL) SAT solvers, which rely on decision-level backtracking and thus lack fine-grained control over the scope of literal unassignments during conflict resolution. To overcome this, the paper introduces a graph-based backtracking mechanism that leverages the implication graph as a guiding structure and incorporates a user-defined weight function to precisely minimize the total weight of literals to be undone. This approach transcends the conventional decision-level backtracking paradigm, subsuming both chronological and non-chronological backtracking as special cases and thereby generalizing the CDCL backtracking framework. Experimental results on the NapSAT solver demonstrate that the proposed method significantly reduces the number of literal propagations and substantially improves solving efficiency.

Abstract

We present graph backtracking, a novel, fine-grained backtracking scheme for CDCL-based SAT solving, parametrized by a user-defined weight function. For conflict repair, we challenge the decision level abstraction and use the implication graph as a precise guiding structure to minimize the weight of literals that are unassigned. Graph backtracking is sound and complete. We show that it is a generalization of chronological and non-chronological backtracking by simulating them with specific weight functions. Our approach is implemented in the experimental solver NapSAT. Empirical results show that graph backtracking requires fewer literal propagations than standard approaches, leading to improved solver runtime.

Problem

• CDCL
• SAT solving
• backtracking
• implication graph
• conflict repair

Innovation

• graph backtracking
• CDCL
• implication graph
• SAT solving
• weight function