Weighted Model Counting with Twin-Width

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GANIAN Robert POKRÝVKA Filip SCHIDLER André SIMONOV Kirill SZEIDER Stefan

Rok publikování 2022
Druh Článek ve sborníku
Konference 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)
Fakulta / Pracoviště MU

Fakulta informatiky

Citace
Doi http://dx.doi.org/10.4230/LIPIcs.SAT.2022.15
Klíčová slova Weighted model counting;twin-width;parameterized complexity;SAT
Popis 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.
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