2026-07-20T04:51:30Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:26316 2026-07-16T10:50:11Z ddc:004 open_access

A Canonical Generalization of OBDD Capelli, Florent Choi, YooJung Mengel, Stefan Muñoz, Martín Van den Broeck, Guy Boolean functions Model counting Knowledge Compilation We introduce Tree Decision Diagrams (TDD) as a model for Boolean functions that generalizes OBDD. They can be seen as a restriction of structured d-DNNF; that is, d-DNNF that respect a vtree T. We show that TDDs enjoy the same tractability properties as OBDD, such as model counting, enumeration, conditioning, and apply, and are more succinct. In particular, we show that CNF formulas of treewidth k can be represented by TDDs of FPT size, which is known to be impossible for OBDD. We study the complexity of compiling CNF formulas into deterministic TDDs via bottom-up compilation and relate the complexity of this approach with the notion of factor width introduced by Bova and Szeider. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Florent Capelli and YooJung Choi and Stefan Mengel and Martín Muñoz and Guy Van den Broeck 2026 Is Part Of LIPIcs, Volume 377, 29th International Conference on Theory and Applications of Satisfiability Testing (SAT 2026) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SAT.2026.10 urn:nbn:de:0030-drops-263167 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2026.10 eng https://creativecommons.org/licenses/by/4.0/legalcode