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A Canonical Generalization of OBDD

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Computer Science > Artificial Intelligence

arXiv:2604.05537 (cs)
[Submitted on 7 Apr 2026]

Title:A canonical generalization of OBDD

Authors:Florent Capelli, YooJung Choi, Stefan Mengel, Martín Muñoz, Guy Van den Broeck
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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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Subjects: Artificial Intelligence (cs.AI); Data Structures and Algorithms (cs.DS)
Cite as: arXiv:2604.05537 [cs.AI]
(or arXiv:2604.05537v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2604.05537

Submission history

From: Florent Capelli [view email]
[v1] Tue, 7 Apr 2026 07:36:21 UTC (387 KB)
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