DEV-TOOLSApril 13, 20261 min read11 views

A Canonical Generalization of OBDD

Researchers introduce Tree Decision Diagrams (TDD), a model that generalizes OBDD with better succinctness while maintaining key tractability properties for Boolean functions.

Computer Science > Artificial Intelligence

Title:A canonical generalization of OBDD

View PDF HTML (experimental)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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