Beyersdorff, O orcid.org/0000-0002-2870-1648, Blinkhorn, J and Hinde, L (2018) Size, Cost and Capacity: A Semantic Technique for Hard Random QBFs. In: Karlin, AR, (ed.) LIPIcs : Leibniz International Proceedings in Informatics. 9th Innovations in Theoretical Computer Science Conference (ITCS 2018), 11-14 Jan 2018, Cambridge, MA, USA. Schloss Dagstuhl - Leibniz-Zentrum für Informatik ISBN 978-3-95977-060-6
Abstract
As a natural extension of the SAT problem, an array of proof systems for quantified Boolean formulas (QBF) have been proposed, many of which extend a propositional proof system to handle universal quantification. By formalising the construction of the QBF proof system obtained from a propositional proof system by adding universal reduction (Beyersdorff, Bonacina & Chew, ITCS'16), we present a new technique for proving proof-size lower bounds in these systems. The technique relies only on two semantic measures: the cost of a QBF, and the capacity of a proof. By examining the capacity of proofs in several QBF systems, we are able to use the technique to obtain lower bounds based on cost alone. As applications of the technique, we first prove exponential lower bounds for a new family of simple QBFs representing equality. The main application is in proving exponential lower bounds with high probability for a class of randomly generated QBFs, the first 'genuine' lower bounds of this kind, which apply to the QBF analogues of resolution, Cutting Planes, and Polynomial Calculus. Finally, we employ the technique to give a simple proof of hardness for a prominent family of QBFs.
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: | © Olaf Beyersdorff, Joshua Blinkhorn, and Luke Hinde; licensed under Creative Commons License CC-BY To view a copy of this license, visit https://creativecommons.org/licenses/by/3.0/. |
Keywords: | quantified Boolean formulas; proof complexity; 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) |
Depositing User: | Symplectic Publications |
Date Deposited: | 01 Nov 2017 17:04 |
Last Modified: | 07 May 2019 01:51 |
Status: | Published |
Publisher: | Schloss Dagstuhl - Leibniz-Zentrum für Informatik |
Identification Number: | 10.4230/LIPIcs.ITCS.2018.9 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:123220 |