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@inproceedings{2215105, author = {Ganian, Robert and Pokrývka, Filip and Schidler, André and Simonov, Kirill and Szeider, Stefan}, address = {Dagstuhl, Germany}, booktitle = {25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)}, doi = {http://dx.doi.org/10.4230/LIPIcs.SAT.2022.15}, editor = {Meel, Kuldeep S. and Strichman, Ofer}, keywords = {Weighted model counting;twin-width;parameterized complexity;SAT}, howpublished = {elektronická verze "online"}, language = {eng}, location = {Dagstuhl, Germany}, isbn = {978-3-95977-242-6}, pages = {"15:1"-"15:17"}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum fur Informatik}, title = {Weighted Model Counting with Twin-Width}, year = {2022} }
TY - JOUR ID - 2215105 AU - Ganian, Robert - Pokrývka, Filip - Schidler, André - Simonov, Kirill - Szeider, Stefan PY - 2022 TI - Weighted Model Counting with Twin-Width PB - Schloss Dagstuhl - Leibniz-Zentrum fur Informatik CY - Dagstuhl, Germany SN - 9783959772426 KW - Weighted model counting;twin-width;parameterized complexity;SAT N2 - 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. ER -
GANIAN, Robert, Filip POKRÝVKA, André SCHIDLER, Kirill SIMONOV a Stefan SZEIDER. Weighted Model Counting with Twin-Width. Online. In Meel, Kuldeep S. and Strichman, Ofer. \textit{25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)}. Dagstuhl, Germany: Schloss Dagstuhl - Leibniz-Zentrum fur Informatik, 2022, s.~''15:1''-''15:17'', 17 s. ISBN~978-3-95977-242-6. Dostupné z: https://dx.doi.org/10.4230/LIPIcs.SAT.2022.15.
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