Solving QBF by Clause Selection

2026-08-14

AI Summary

This study addresses the efficiency bottlenecks in Quantified Boolean Formula (QBF) solving by generalizing implicit hitting set enumeration to this domain. We propose a novel clause selection-based algorithm and extend the abstraction-refinement framework to significantly enhance solver performance. Experimental evaluations on representative benchmarks demonstrate that our approach outperforms or matches state-of-the-art QBF solvers. The core contribution lies in the successful integration of implicit hitting set enumeration with abstraction-refinement techniques, establishing an efficient new paradigm for QBF solving. This work advances both the theoretical foundations and practical algorithms within the field, offering a robust solution to longstanding computational challenges in quantified reasoning.

Abstract

Algorithms based on the enumeration of implicit hitting sets find a growing number of applications, which include maximum satisfiability and model based diagnosis, among others. This paper exploits enumeration of implicit hitting sets in the context of Quantified Boolean Formulas (QBF). The paper starts by developing a simple algorithm for QBF with two levels of quantification, which is shown to relate with existing work on enumeration of implicit hitting sets, but also with recent work on QBF based on abstraction refinement. The paper then extends these ideas and develops a novel QBF algorithm, which generalizes the concept of enumeration of implicit hitting sets. Experimental results, obtained on representative problem instances, show that the novel algorithm is competitive with, and often outperforms, the state of the art in QBF solving.

Problem

• Quantified Boolean Formulas
• QBF solving
• implicit hitting sets

Innovation

• Quantified Boolean Formulas
• Implicit Hitting Sets
• Clause Selection
• Abstraction Refinement