Guiding real-world SAT solving with dynamic hypergraph separator decomposition
Why this work is in the frame
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Bibliographic record
Abstract
The general solution of satisfiability problems is NP-complete. Although state-of-the-art SAT solvers can efficiently obtain the solutions of many real-world instances, there are still a large number of real-world SAT families which cannot be solved in reasonable time. Much effort has been spent to take advantage of the internal structure of SAT instances. Existing decomposition techniques are based on preprocessing the static structure of the original problem. We present a dynamic decomposition method based on hypergraph separators. Integrating the separator decomposition into the variable ordering of a modern SAT solver leads to speedups on large real-world satisfiability problems. Compared with a static decomposition based variable ordering, such as Dtree (Huang and Darwiche, 2003), our approach does not need time to construct the full tree decomposition, which sometimes needs more time than the solving process itself. Our primary focus is to achieve speedups on large real-world satisfiability problems. Our results show that the new solver often outperforms both regular zChaff and zChaff integrated with Dtree decomposition. The dynamic separator decomposition shows promise in that it significantly decreases the number of decisions for some real-world problems.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it