Beyersdorff, O orcid.org/0000-0002-2870-1648, Hinde, L and Pich, J (2018) Reasons for Hardness in QBF Proof Systems. In: 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017). 37th IARCS Annual Conference (FSTTCS 2017), 11-15 Dec 2017, Kanpur, India. Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik , 14:1-14:15. ISBN 978-3-95977-055-2
Abstract
We aim to understand inherent reasons for lower bounds for QBF proof systems, and revisit and compare two previous approaches in this direction.The first of these relates size lower bounds for strong QBF Frege systems to circuit lower bounds via strategy extraction Beyersdorff & Pich, LICS’16). Here we show a refined version of strategy extraction and thereby for any QBF proof system obtain a trichotomy for hardness: (1) via circuit lower bounds, (2) via propositional Resolution lower bounds, or (3) ‘genuine’ QBF lower bounds. The second approach tries to explain QBF lower bounds through quantifier alternations in a system called relaxing QU-Res (Chen, ICALP’16). We prove a strong lower bound for relaxing QU-Res, which also exhibits significant shortcomings of that model. Prompted by this we propose an alternative, improved version, allowing more flexible oracle queries in proofs. We show that lower bounds in our new model correspond to the trichotomy obtained via strategy extraction.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) Olaf Beyersdorff, Luke Hinde, and Ján Pich; licensed under Creative Commons License CC-BY. (https://creativecommons.org/licenses/by/3.0/) |
Keywords: | proof complexity; quantified Boolean formulas; resolution; lower bounds |
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 John Templeton Foundation - DO NOT USE 48138 |
Depositing User: | Symplectic Publications |
Date Deposited: | 01 Nov 2017 17:03 |
Last Modified: | 23 Jun 2023 22:38 |
Status: | Published |
Publisher: | Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik |
Identification Number: | 10.4230/LIPIcs.FSTTCS.2017.14 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:123218 |