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A Canonical Generalization of OBDD

Authors Florent Capelli , YooJung Choi , Stefan Mengel , Martín Muñoz , Guy Van den Broeck

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Subject Classification

ACM Subject Classification
  • Computing methodologies → Knowledge representation and reasoning
  • Theory of computation → Constraint and logic programming
Keywords
  • Boolean functions
  • Model counting
  • Knowledge Compilation

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Abstract

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.

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Florent Capelli, YooJung Choi, Stefan Mengel, Martín Muñoz, and Guy Van den Broeck. A Canonical Generalization of OBDD. In 29th International Conference on Theory and Applications of Satisfiability Testing (SAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 377, pp. 10:1-10:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.SAT.2026.10

Author Details

Florent Capelli
  • Univ. Artois, CNRS, UMR 8188, CRIL, F-62300 Lens, France
YooJung Choi
  • Arizona State University, Tempe, AZ, USA
Stefan Mengel
  • Univ. Artois, CNRS, UMR 8188, CRIL, F-62300 Lens, France
Martín Muñoz
  • Univ. Artois, CNRS, UMR 8188, CRIL, F-62300 Lens, France
Guy Van den Broeck
  • University of California, Los Angeles, CA, USA

Funding

  • Capelli, Florent: ANR-25-CE23-3078 CERADOC.
  • Choi, YooJung: AFOSR grant FA9550-25-1-0320.
  • Mengel, Stefan: ANR-25-CE23-3078 CERADOC.
  • Van den Broeck, Guy: DARPA ANSR program under award FA8750-23-2-0004.

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