Beyersdorff, O, Chew, L, Mahajan, M et al. (1 more author) (2016) Are Short Proofs Narrow? QBF Resolution is not Simple. In: Ollinger, N and Vollmer, H, (eds.) 33rd Symposium on Theoretical Aspects of Computer Science (STACS'16). Symposium on Theoretical Aspects of Computer Science (STACS'16), 17-20 Feb 2016, Orleans, France. Schloss Dagstuhl - Leibniz-Zentrum für Informatik ISBN 978-3-95977-001-9
Abstract
The groundbreaking paper ‘Short proofs are narrow – resolution made simple’ by Ben-Sasson and Wigderson (J. ACM 2001) introduces what is today arguably the main technique to obtain resolution lower bounds: to show a lower bound for the width of proofs. Another important measure for resolution is space, and in their fundamental work, Atserias and Dalmau (J. Comput. Syst. Sci. 2008) show that space lower bounds again can be obtained via width lower bounds. Here we assess whether similar techniques are effective for resolution calculi for quantified Boolean formulas (QBF). A mixed picture emerges. Our main results show that both the relations between size and width as well as between space and width drastically fail in Q-resolution, even in its weaker tree-like version. On the other hand, we obtain positive results for the expansion-based resolution systems Exp+Res and IR-calc, however only in the weak tree-like models. Technically, our negative results rely on showing width lower bounds together with simultaneous upper bounds for size and space. For our positive results we exhibit space and width preserving simulations between QBF resolution calculi.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Editors: |
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Copyright, Publisher and Additional Information: | © 2015, Olaf Beyersdorff, Leroy Chew, Meena Mahajan, and Anil Shukla; licensed under Creative Commons License CC-BY |
Keywords: | Proof complexity; QBF; resolution; lower bound techniques |
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) |
Funding Information: | Funder Grant number EPSRC EP/L024233/1 John Templeton Foundation - DO NOT USE 48138 |
Depositing User: | Symplectic Publications |
Date Deposited: | 10 Dec 2015 14:53 |
Last Modified: | 10 Mar 2016 08:20 |
Published Version: | http://dx.doi.org/10.4230/LIPIcs.STACS.2016.15 |
Status: | Published |
Publisher: | Schloss Dagstuhl - Leibniz-Zentrum für Informatik |
Identification Number: | 10.4230/LIPIcs.STACS.2016.15 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:92569 |