A Canonical Generalization of OBDD

Smarter logic charts promise speed and smaller size — commenters demand a demo

TLDR: Researchers propose Tree Decision Diagrams, promising the same handy tricks as classic logic diagrams but in smaller packages for certain problems. Commenters are split between “cool—show me the code and CUDD benchmarks” and “explain why this matters,” turning a theory paper into a GitHub‑hunt and ELI5 showdown.

New paper alert: researchers unveil Tree Decision Diagrams (TDDs), think “tidier, smarter flowcharts” for yes/no logic problems. They claim TDDs keep the crowd‑pleasing perks of the classic OBDDs (a beloved way to reason about logic): fast counting of solutions, listing them, updating with known values, and combining pieces. The twist? TDDs can be more compact, especially when your problem has a tree‑like structure; the authors say they can stay small where OBDDs famously bloat. That’s a big deal for everything from chip verification to AI planning, where size = speed.

But the real show is the comments. One user cheers, “finally, theory on the HN front page,” then immediately bangs the drum we all hear: where’s the code and how does it stack up against legendary BDD library [CUDD]? Another jumps in with the eternal HN chorus: ELI5, please—why should non‑logicians care? The thread splits into two camps: the “GitHub or it didn’t happen” skeptics demanding benchmarks, and the explain‑it‑like‑I’m‑five crowd begging for a plain‑English pitch. Jokes fly about flowcharts versus “flow‑charlatans,” while nostalgic veterans reminisce about the BDD days and wonder if TDDs are the sequel we’ve been waiting for—or just another theory drop without a repo. Either way, this paper has the peanut gallery buzzing.

Key Points

  • Tree Decision Diagrams (TDD) are introduced as a Boolean function model that generalizes OBDDs and is a restriction of structured d-DNNF respecting a vtree.
  • TDDs retain OBDD-like tractable operations, including model counting, enumeration, conditioning, and the apply operator.
  • TDDs are shown to be more succinct than OBDDs.
  • CNF formulas with treewidth k can be represented by TDDs of fixed-parameter tractable (FPT) size, unlike with OBDDs.
  • The complexity of bottom-up compilation of CNFs into deterministic TDDs is analyzed and linked to the factor width parameter introduced by Bova and Szeider.

Hottest takes

"Positively surprised to see stuff like these on HN first page!" — gignico
"do you have an implementation that can be compared with CUDD and similar BDD libraries?" — gignico
"Can someone give a quick explanation of why this is important?" — throwaway81523
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