Beyersdorff, O, Chew, L and Janota, M (2015) Proof complexity of resolution-based QBF calculi. In: LIPI Symposium on Theoretical Aspects of Computer Science (STACS'15). 32nd International Symposium on Theoretical Aspects of Computer Science, 04 Mar 2015 Schloss Dagstuhl - Leibniz International Proceedings in Informatics , 76 - 89. ISBN 9783939897781
Abstract
Proof systems for quantified Boolean formulas (QBFs) provide a theoretical underpinning for the performance of important QBF solvers. However, the proof complexity of these proof systems is currently not well understood and in particular lower bound techniques are missing. In this paper we exhibit a new and elegant proof technique for showing lower bounds in QBF proof systems based on strategy extraction. This technique provides a direct transfer of circuit lower bounds to lengths of proofs lower bounds. We use our method to show the hardness of a natural class of parity formulas for Q-resolution and universal Q-resolution. Variants of the formulas are hard for even stronger systems as long-distance Q-resolution and extensions. With a completely different lower bound argument we show the hardness of the prominent formulas of Kleine Büning et al. [34] for the strong expansion-based calculus IR-calc. Our lower bounds imply new exponential separations between two different types of resolution-based QBF calculi: proof systems for CDCLbased solvers (Q-resolution, long-distance Q-resolution) and proof systems for expansion-based solvers (∀Exp+Res and its generalizations IR-calc and IRM-calc). The relations between proof systems from the two different classes were not known before.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2015, Olaf Beyersdorff, Leroy Chew, and Mikoláš Janota; licensed under Creative Commons License CC-BY. |
Keywords: | Lower bound techniques; Proof complexity; QBF; Separations |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) > Institute for Computational and Systems Science (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 26 Oct 2015 11:49 |
Last Modified: | 26 Oct 2015 11:49 |
Published Version: | http://dx.doi.org/10.4230/LIPIcs.STACS.2015.76 |
Status: | Published |
Publisher: | Schloss Dagstuhl - Leibniz International Proceedings in Informatics |
Identification Number: | 10.4230/LIPIcs.STACS.2015.76 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:85608 |