
QRAT Polynomially Simulates Merge Resolution
Merge Resolution (MRes [Beyersdorff et al. J. Autom. Reason.'2021] ) is ...
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Proof Complexity of Symbolic QBF Reasoning
We introduce and investigate symbolic proof systems for Quantified Boole...
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SizeDegree TradeOffs for SumsofSquares and Positivstellensatz Proofs
We show that if a system of degreek polynomial inequalities on n Boolea...
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Short Proofs for Some Symmetric Quantified Boolean Formulas
We exploit symmetries to give short proofs for two prominent formula fam...
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SemiAlgebraic Proofs, IPS Lower Bounds and the τConjecture: Can a Natural Number be Negative?
We introduce the binary value principle which is a simple subsetsum ins...
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Towards Understanding and Harnessing the Potential of Clause Learning
Efficient implementations of DPLL with the addition of clause learning a...
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Generating Schemata of Resolution Proofs
Two distinct algorithms are presented to extract (schemata of) resolutio...
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Hard QBFs for Merge Resolution
We prove the first proof size lower bounds for the proof system Merge Resolution (MRes [Olaf Beyersdorff et al., 2020]), a refutational proof system for prenex quantified Boolean formulas (QBF) with a CNF matrix. Unlike most QBF resolution systems in the literature, proofs in MRes consist of resolution steps together with information on countermodels, which are syntactically stored in the proofs as merge maps. As demonstrated in [Olaf Beyersdorff et al., 2020], this makes MRes quite powerful: it has strategy extraction by design and allows short proofs for formulas which are hard for classical QBF resolution systems. Here we show the first exponential lower bounds for MRes, thereby uncovering limitations of MRes. Technically, the results are either transferred from bounds from circuit complexity (for restricted versions of MRes) or directly obtained by combinatorial arguments (for full MRes). Our results imply that the MRes approach is largely orthogonal to other QBF resolution models such as the QCDCL resolution systems QRes and QURes and the expansion systems ∀Exp+Res and IR.
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