A canonical generalization of OBDD

TL;DR

This paper introduces Tree Decision Diagrams (TDD), a generalization of OBDD, which are more succinct and maintain key tractability properties, enabling efficient representation and compilation of complex Boolean functions.

Contribution

The paper defines TDD as a new model that generalizes OBDD, demonstrating their efficiency and applicability to CNF formulas of bounded treewidth, surpassing OBDD capabilities.

Findings

TDDs are more succinct than OBDD for certain formulas.

TDDs retain key tractability properties like model counting and conditioning.

CNF formulas of treewidth k can be represented by TDDs of FPT size.

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.