Beyersdorff, O orcid.org/0000-0002-2870-1648, Blinkhorn, J and Mahajan, M (2021) Building Strategies into QBF Proofs. Journal of Automated Reasoning, 65 (2). pp. 125-154. ISSN 0168-7433
Abstract
Strategy extraction is of great importance for quantified Boolean formulas (QBF), both in solving and proof complexity. So far in the QBF literature, strategy extraction has been algorithmically performed from proofs. Here we devise the first QBF system where (partial) strategies are built into the proof and are piecewise constructed by simple operations along with the derivation. This has several advantages: (1) lines of our calculus have a clear semantic meaning as they are accompanied by semantic objects; (2) partial strategies are represented succinctly (in contrast to some previous approaches); (3) our calculus has strategy extraction by design; and (4) the partial strategies allow new sound inference steps which are disallowed in previous central QBF calculi such as Q-Resolution and long-distance Q-Resolution. The last item (4) allows us to show an exponential separation between our new system and the previously studied reductionless long-distance resolution calculus. Our approach also naturally lifts to dependency QBFs (DQBF), where it yields the first sound and complete CDCL-style calculus for DQBF, thus opening future avenues into CDCL-based DQBF solving.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2020. Building Strategies into QBF Proofs This is an open access article under the terms of the Creative Commons Attribution 4.0 International (CC BY 4.0) (https://creativecommons.org/licenses/by/4.0/) |
Keywords: | QBF; DQBF; Resolution; Proof complexity |
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: | 02 Jul 2020 11:40 |
Last Modified: | 25 Jun 2023 22:20 |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/s10817-020-09560-1 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:162591 |
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