Year: 2026
Type: preprint
Abstract: Tree Decision Diagrams (TDDs) are a data structure recently introduced by Capelli et al. (SAT 2026). They are structured along a vtree and the size of their canonical form lies between Ordered Binary Decision Diagrams (OBDDs) and deterministic structured DNNF circuits (d-SDNNFs). While the succinctness gap between TDD and d-SDNNF is exponential, only a quasipolynomial separation between OBDD and TDD has been shown and it was left as open question whether this is optimal. We answer this question affirmatively by showing that every TDD can be transformed to an equivalent OBDD of quasipolynomial size. Although this might be seen as a weakness, our second result shows that TDDs share another desirable property with OBDDs that is not known to hold for d-SDNNF: Given a TDD and another target vtree, it is possible to construct the minimal and canonical TDD respecting the new vtree in time polynomial in the input and output. As a result we also obtain that the equivalence test between TDDs over different vtrees can be done in polynomial time.
Source: arXiv (Cornell University)
Institutions: Technische Universität Ilmenau, Durham University
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W7213945296
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