# Evaluating QBF Solvers: Quantifier Alternations Matter

## TL;DR

This paper empirically investigates how the number of quantifier alternations in QBFs affects solver performance, emphasizing the importance of considering alternations for evaluating and developing diverse solving paradigms.

## Contribution

It provides experimental evidence that solver performance varies with quantifier alternations, advocating for evaluation methods that account for this factor and exploring combined solving approaches.

## Key findings

- Solver performance varies significantly with quantifier alternations.
- Different solving paradigms excel at different levels of alternation complexity.
- Highlighting the need for evaluation methods that incorporate quantifier alternations.

## Abstract

We present an experimental study of the effects of quantifier alternations on the evaluation of quantified Boolean formula (QBF) solvers. The number of quantifier alternations in a QBF in prenex conjunctive normal form (PCNF) is directly related to the theoretical hardness of the respective QBF satisfiability problem in the polynomial hierarchy. We show empirically that the performance of solvers based on different solving paradigms substantially varies depending on the numbers of alternations in PCNFs. In related theoretical work, quantifier alternations have become the focus of understanding the strengths and weaknesses of various QBF proof systems implemented in solvers. Our results motivate the development of methods to evaluate orthogonal solving paradigms by taking quantifier alternations into account. This is necessary to showcase the broad range of existing QBF solving paradigms for practical QBF applications. Moreover, we highlight the potential of combining different approaches and QBF proof systems in solvers.