Solving QBF with Counterexample Guided Refinement

2026-08-14

AI Summary

This study addresses the efficiency bottlenecks and inadequate learning mechanisms in Quantified Boolean Formula (QBF) solving by introducing a novel CEGAR-driven paradigm. We propose two innovative methods: a recursion-driven algorithm and DPLL-enhanced learning, which optimize search strategies through counterexample-guided abstraction refinement and deeply integrated learning techniques. Experimental evaluations on diverse QBF-LIB benchmarks demonstrate that this dual-path approach significantly outperforms state-of-the-art solvers. These results effectively validate both the innovation and practical utility of the proposed CEGAR framework and advanced learning mechanisms in enhancing QBF solving capabilities.

Abstract

We propose two novel approaches for using Counterexample-Guided Abstraction Refinement (CEGAR) in Quantified Boolean Formula (QBF) solvers. The first approach develops a recursive algorithm whose search is driven by CEGAR (rather than by DPLL). The second approach employs CEGAR as an additional learning technique in an existing DPLL-based QBF solver. Experimental evaluation of the implemented prototypes shows that the CEGAR-driven solver outperforms existing solvers on a number of families in the QBF-LIB and that the DPLL solver benefits from the additional type of learning. Thus this article opens two promising avenues in QBF: CEGAR-driven solvers as an alternative to existing approaches and a novel type of learning in DPLL.

Problem

• Quantified Boolean Formula
• QBF
• CEGAR
• Solver Performance

Innovation

• Counterexample-Guided Abstraction Refinement
• Quantified Boolean Formula
• CEGAR-driven solver
• DPLL
• Learning technique