Lift TDD restructuring and equivalence testing to SDDs and d-SDNNFs

Determine whether restructuring in time polynomial in the input and output, or polynomial-time equivalence testing, can be extended from Tree Decision Diagrams to sentential decision diagrams or to all deterministic structured decomposable negation normal forms.

Background

The paper establishes two efficient properties for Tree Decision Diagrams (TDDs): restructuring a TDD to an arbitrary target vtree in time polynomial in the input and output sizes, and testing equivalence between TDDs over different vtrees in polynomial time. The authors note that analogous results are not established for more succinct structured representation formats, particularly sentential decision diagrams (SDDs) and deterministic structured decomposable negation normal forms (d-SDNNFs).

References

With that said, there are still several open research questions: first of all, can either restructuring in time polynomial in the input and output or the polynomial time equivalence test be lifted to SDDs or even all d-SDNNFs?

— Restructuring Tree Decision Diagrams  (2609.21842 - Berkholz et al., 18 Sep 2026) in Section 5, Conclusion