Structure-Aware Lower Bounds and Broadening the Horizon of Tractability for QBF

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...

Full description

Saved in:
Bibliographic Details
Published in:2023 38TH ANNUAL ACM/IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE, LICS pp. 1 - 14
Main Authors: Fichte, Johannes K., Ganian, Robert, Hecher, Markus, Slivovsky, Friedrich, Ordyniak, Sebastian
Format: Conference Proceeding
Language:English
Published: IEEE 26.06.2023
Series:IEEE Symposium on Logic in Computer Science
Subjects:
Complexity theory
Computer science
Filling
Probabilistic logic
Structural engineering
Upper bound
ISBN:9798350335880, 9798350335873
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISBN:9798350335880
9798350335873
DOI:10.1109/LICS56636.2023.10175675