Semi-Algebraic Proof Systems for QBF
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914150724141056 |
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| author | Beyersdorff, Olaf Bonacina, Ilario Kasche, Kaspar Mahajan, Meena Spachmann, Luc Nicolas |
| author_facet | Beyersdorff, Olaf Bonacina, Ilario Kasche, Kaspar Mahajan, Meena Spachmann, Luc Nicolas |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_08050 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Semi-Algebraic Proof Systems for QBF Beyersdorff, Olaf Bonacina, Ilario Kasche, Kaspar Mahajan, Meena Spachmann, Luc Nicolas Logic in Computer Science Computational Complexity Logic 03F20, 03D15 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. |
| title | Semi-Algebraic Proof Systems for QBF |
| topic | Logic in Computer Science Computational Complexity Logic 03F20, 03D15 |
| url | https://arxiv.org/abs/2511.08050 |