An Efficient Two-phase Method for Prime Compilation of Non-clausal Boolean Formulae
Bibliographic record
Abstract
Prime compilation aims to generate all prime implicates/implicants of a Boolean formula. Recently, prime compilation of non-clausal formulae has received great attention. Since it is hard for$\Sigma_{2}^{P}$, existing methods have performance issues. We argue that the main performance bottleneck stems from enlarging the search space using dual rail (DR) encoding, and computing a minimal clausal formula as a by-product. To deal with the issue, we propose a two-phase approach, namely CoAPI, for prime compilation of non-clausal formulae. Thanks to the two-phase framework, we construct a clausal formula without using DR encoding. In addition, to improve performance, the key in our work is a novel bounded prime extraction (BPE) method that, interleaving extracting prime implicates with extracting small implicates, enables constructing a succinct clausal formula rather than a minimal one. Following the assessment way of the state-of-the-art (SOTA) work, we show that CoAPI achieves SOTA performance. Particularly, for generating all prime implicates, CoAPI is up to about one order of magnitude faster. Moreover, we evaluate CoAPI on a benchmark sourcing from real-world industries. The results also confirm the outperformance of CoAPI11Our code and benchmarks are publicly available at https://github.com/LuoWeiLinWillam/CoAPI.
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.007 | 0.002 |
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".