Fichte, JK, Ganian, R, Hecher, M et al. (2 more authors) (2023) Structure-Aware Lower Bounds and Broadening the Horizon of Tractability for QBF. In: 2023 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS). 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), 26-29 Jun 2023, Boston, USA. IEEE ISBN 979-8-3503-3587-3
Abstract
The QSAT problem, which asks to evaluate a quantified Boolean formula (QBF), is of fundamental interest in approximation, counting, decision, and probabilistic complexity and is also considered the prototypical PSPACE-complete problem. As such, it has previously been studied under various structural restrictions (parameters), most notably parameterizations of the primal graph representation of instances. Indeed, it is known that QSAT remains PSPACE-complete even when restricted to instances with constant treewidth of the primal graph, but the problem admits a double-exponential fixed-parameter algorithm parameterized by the vertex cover number (primal graph).However, prior works have left a gap in our understanding of the complexity of QSAT when viewed from the perspective of other natural representations of instances, most notably via incidence graphs. In this paper, we develop structure-aware reductions which allow us to obtain essentially tight lower bounds for highly restricted instances of QSAT, including instances whose incidence graphs have bounded treedepth or feedback vertex number. We complement these lower bounds with novel algorithms for QSAT which establish a nearly-complete picture of the problem's complexity under standard graph-theoretic parameterizations. We also show implications for other natural graph representations, and obtain novel upper as well as lower bounds for QSAT under more fine-grained parameterizations of the primal graph.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. |
Keywords: | Computer science, Upper bound, Probabilistic logic, Filling, Complexity theory, Structural engineering, Standards |
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 (Engineering and Physical Sciences Research Council) EP/V00252X/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 26 Apr 2023 13:58 |
Last Modified: | 06 Dec 2024 16:37 |
Status: | Published |
Publisher: | IEEE |
Identification Number: | 10.1109/LICS56636.2023.10175675 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:198609 |