Some algorithmic and complexity results for monotone Boolean duality (hypergraph transversal)
Bibliographic record
Abstract
Let y be a monotone CNF formula and let 4 be a monotone DNF formula. The problem of determining in polynomial time in the size of y and 4 whether y uharr;a=4 uharr; a for all assignments alpha (known as DUAL) has been a longstanding open problem. We show that two popular families of algorithms for DUAL (Berge's Sequential Method and Fredman and Khachiyan's Algorithm A) are really restrictions of the DPLL class of algorithms which has long been studied in relation to SAT. We also present super-polynomial lower bounds for DPLL on two classes of read-once formulae. Finally, we present DPLLCache, DPLL with memorization, and show that DPLLCache is strictly stronger than DPLL and therefore also the Sequential Method and Algorithm A. In fact, we show that DPLLCache can solve all read-once formulae using polynomial size decision trees.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.015 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.003 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.005 | 0.011 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.008 |
| Insufficient payload (model declined to judge) | 0.011 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".