Beyersdorff, O orcid.org/0000-0002-2870-1648, Blinkhorn, J, Chew, L et al. (2 more authors) (2019) Reinterpreting Dependency Schemes: Soundness Meets Incompleteness in DQBF. Journal of Automated Reasoning, 63 (3). pp. 597-623. ISSN 0168-7433
Abstract
Dependency quantified Boolean formulas (DQBF) and QBF dependency schemes have been treated separately in the literature, even though both treatments extend QBF by replacing the linear order of the quantifier prefix with a partial order. We propose to merge the two, by reinterpreting a dependency scheme as a mapping from QBF into DQBF. Our approach offers a fresh insight on the nature of soundness in proof systems for QBF with dependency schemes, in which a natural property called ‘full exhibition’ is central. We apply our approach to QBF proof systems from two distinct paradigms, termed ‘universal reduction’ and ‘universal expansion’. We show that full exhibition is sufficient (but not necessary) for soundness in universal reduction systems for QBF with dependency schemes, whereas for expansion systems the same property characterises soundness exactly. We prove our results by investigating DQBF proof systems, and then employing our reinterpretation of dependency schemes. Finally, we show that the reflexive resolution path dependency scheme is fully exhibited, thereby proving a conjecture of Slivovsky.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018, The Author(s). This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
Keywords: | Quantified Boolean formulas; DQBF; Dependency schemes |
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) |
Depositing User: | Symplectic Publications |
Date Deposited: | 09 Nov 2018 14:27 |
Last Modified: | 25 Jun 2023 21:35 |
Status: | Published |
Publisher: | Springer Netherlands |
Identification Number: | 10.1007/s10817-018-9482-4 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:138399 |
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