Researchers have introduced Tree Decision Diagrams (TDD) as a novel model for Boolean functions that generalizes OBDD technology. These diagrams operate as restricted structured d-DNNF that respect a vtree T structure. While maintaining the same tractability properties as OBDDs—including model counting, enumeration, conditioning, and apply operations—TDDs offer more succinct representations for complex logical functions.

A breakthrough finding shows CNF formulas of treewidth k can be represented by TDDs of FPT size, a capability proven impossible for traditional OBDDs. This advancement enables more efficient representation of complex logical structures while preserving computational tractability across essential operations. The research establishes TDDs as a superior alternative for representing Boolean functions with specific structural properties.