License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SAT.2022.15
URN: urn:nbn:de:0030-drops-166896
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16689/
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Ganian, Robert ; Pokrývka, Filip ; Schidler, André ; Simonov, Kirill ; Szeider, Stefan

Weighted Model Counting with Twin-Width

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Abstract

Bonnet et al. (FOCS 2020) introduced the graph invariant twin-width and showed that many NP-hard problems are tractable for graphs of bounded twin-width, generalizing similar results for other width measures, including treewidth and clique-width. In this paper, we investigate the use of twin-width for solving the propositional satisfiability problem (SAT) and propositional model counting. We particularly focus on Bounded-ones Weighted Model Counting (BWMC), which takes as input a CNF formula F along with a bound k and asks for the weighted sum of all models with at most k positive literals. BWMC generalizes not only SAT but also (weighted) model counting.
We develop the notion of "signed" twin-width of CNF formulas and establish that BWMC is fixed-parameter tractable when parameterized by the certified signed twin-width of F plus k. We show that this result is tight: it is neither possible to drop the bound k nor use the vanilla twin-width instead if one wishes to retain fixed-parameter tractability, even for the easier problem SAT. Our theoretical results are complemented with an empirical evaluation and comparison of signed twin-width on various classes of CNF formulas.

BibTeX - Entry

@InProceedings{ganian_et_al:LIPIcs.SAT.2022.15,
  author =	{Ganian, Robert and Pokr\'{y}vka, Filip and Schidler, Andr\'{e} and Simonov, Kirill and Szeider, Stefan},
  title =	{{Weighted Model Counting with Twin-Width}},
  booktitle =	{25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)},
  pages =	{15:1--15:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-242-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{236},
  editor =	{Meel, Kuldeep S. and Strichman, Ofer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16689},
  URN =		{urn:nbn:de:0030-drops-166896},
  doi =		{10.4230/LIPIcs.SAT.2022.15},
  annote =	{Keywords: Weighted model counting, twin-width, parameterized complexity, SAT}
}

Keywords: Weighted model counting, twin-width, parameterized complexity, SAT
Collection: 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)
Issue Date: 2022
Date of publication: 28.07.2022
Supplementary Material: Dataset: https://doi.org/10.5281/zenodo.6610819

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