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arXiv · 2511.08050

Semi-Algebraic Proof Systems for QBF

Olaf Beyersdorff·Ilario Bonacina·Kaspar Kasche·Meena Mahajan·Luc Nicolas Spachmann
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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.

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Olaf Beyersdorff, Ilario Bonacina, Kaspar Kasche, Meena Mahajan, Luc Nicolas Spachmann. 2025-11-11. Semi-Algebraic Proof Systems for QBF. https://arxiv.org/abs/2511.08050

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