Semi-Algebraic Proof Systems for QBF
Logic in Computer Science
2025-11-12 v1 Computational Complexity
Logic
Abstract
We introduce new semi-algebraic proof systems for Quantified Boolean Formulas (QBF) analogous to the propositional systems Nullstellensatz, Sherali-Adams and Sum-of-Squares. We transfer to this setting techniques both from the QBF literature (strategy extraction) and from propositional proof complexity (size-degree relations and pseudo-expectation). We obtain a number of strong QBF lower bounds and separations between these systems, even when disregarding propositional hardness.
Cite
@article{arxiv.2511.08050,
title = {Semi-Algebraic Proof Systems for QBF},
author = {Olaf Beyersdorff and Ilario Bonacina and Kaspar Kasche and Meena Mahajan and Luc Nicolas Spachmann},
journal= {arXiv preprint arXiv:2511.08050},
year = {2025}
}