Beyersdorff, O orcid.org/0000-0002-2870-1648, Chew, L, Mahajan, M et al. (1 more author) (2018) Are Short Proofs Narrow? QBF Resolution is not so Simple. ACM Transactions on Computational Logic, 19 (1). 1. ISSN 1529-3785
Abstract
The ground-breaking 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 lower bounds for space again can be obtained via lower bounds for width. In this article, we assess whether similar techniques are effective for resolution calculi for quantified Boolean formulas (QBFs). There are a number of different QBF resolution calculi like Q-resolution (the classical extension of propositional resolution to QBF) and the more recent calculi ∀Exp+Res and IR-calc. For these systems, a mixed picture emerges. Our main results show that the relations both between size and width and 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: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017, the authors. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in ACM Transactions on Computational Logic (TOCL), 19 (1), January 2018, http://doi.acm.org/0.1145/3157053. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Algorithms, Theory, Proof complexity, QBF, resolution, lower bound techniques, simulations |
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) |
Funding Information: | Funder Grant number EPSRC EP/L024233/1 John Templeton Foundation - DO NOT USE 48138 EU - European Union 612638 |
Depositing User: | Symplectic Publications |
Date Deposited: | 01 Nov 2017 16:54 |
Last Modified: | 24 Jan 2018 22:03 |
Status: | Published |
Publisher: | Association for Computing Machinery (ACM) |
Identification Number: | 10.1145/3157053 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:123219 |