ECCC-Report TR20-188https://eccc.weizmann.ac.il/report/2020/188Comments and Revisions published for TR20-188en-usFri, 26 Jan 2024 20:12:24 +0200
Revision 1
| Hard QBFs for Merge Resolution |
Olaf Beyersdorff,
Joshua Blinkhorn,
Meena Mahajan,
Tomáš Peitl,
Gaurav Sood
https://eccc.weizmann.ac.il/report/2020/188#revision1We prove the first genuine QBF 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 genuine QBF 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.Fri, 26 Jan 2024 20:12:24 +0200https://eccc.weizmann.ac.il/report/2020/188#revision1
Paper TR20-188
| Hard QBFs for Merge Resolution |
Olaf Beyersdorff,
Joshua Blinkhorn,
Meena Mahajan,
Tomáš Peitl,
Gaurav Sood
https://eccc.weizmann.ac.il/report/2020/188We 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.Sun, 20 Dec 2020 13:56:21 +0200https://eccc.weizmann.ac.il/report/2020/188