Semi-Algebraic Proof Systems for QBF
By: Olaf Beyersdorff , Ilario Bonacina , Kaspar Kasche and more
Potential Business Impact:
Proves hard computer problems faster than before.
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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