SAT backdoors: Depth beats size

For several decades, much effort has been put into identifying classes of CNF formulas whose satisfiability can be decided in polynomial time. Classic results are the linear-time tractability of Horn formulas (Aspvall, Plass, and Tarjan, 1979) and Krom (i.e., 2CNF) formulas (Dowling and Gallier, 198...

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Bibliographic Details
Published in:Journal of computer and system sciences Vol. 142; p. 103520
Main Authors: Dreier, Jan, Ordyniak, Sebastian, Szeider, Stefan
Format: Journal Article
Language:English
Published: Elsevier Inc 01.06.2024
Subjects:
Backdoor
Elimination distance
Parameterized algorithms
SAT
Satisfiability
Elimination distance
Backdoor
Parameterized algorithms
Satisfiability
SAT
ISSN:0022-0000, 1090-2724
Online Access:Get full text
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Summary:For several decades, much effort has been put into identifying classes of CNF formulas whose satisfiability can be decided in polynomial time. Classic results are the linear-time tractability of Horn formulas (Aspvall, Plass, and Tarjan, 1979) and Krom (i.e., 2CNF) formulas (Dowling and Gallier, 1984). Backdoors, introduced by Williams, Gomes and Selman (2003), gradually extend such a tractable class to all formulas of bounded distance to the class. Backdoor size provides a natural but rather crude distance measure between a formula and a tractable class. Backdoor depth, introduced by Mählmann, Siebertz, and Vigny (2021), is a more refined distance measure, which admits the utilization of different backdoor variables in parallel. We propose FPT approximation algorithms to compute backdoor depth into the classes Horn and Krom. This leads to a linear-time algorithm for deciding the satisfiability of formulas of bounded backdoor depth into these classes.
ISSN:0022-0000
1090-2724
DOI:10.1016/j.jcss.2024.103520