New Encoding for Translating Pseudo-Boolean Constraints into SAT.
Bibliographic record
Abstract
A Pseudo-Boolean (PB) constraint is a linear arithmetic constraint over Boolean variables. PB constraints are and widely used in declarative languages for expressing NP-hard search problems. While there are solvers for sets of PB constraints, there are also reasons to be interested in transforming these to propositional CNF formulas, and a number of methods for doing this have been reported. We introduce a new, two-step, method for transforming PB constraints to propositional CNF formulas. The first step re-writes each PB constraint as a conjunction of PB-Mod constraints, and the second transforms each PB-Mod constraint to CNF. The resulting CNF formulas are compact, and make effective use of unit propagation, in that unit propagation can derive facts from these CNF formulas which it cannot derive from the CNF formulas produced by other commonlyused transformation. We present a preliminary experimental evaluation of the method, using instances of the number partitioning problem as a benchmark set, which indicates that our method out-performs other transformations to CNF when the coefficients of the PB constraints are not small.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.016 | 0.004 |
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".