Balanced covering arrays: A classification of covering arrays and packing arrays via exact methods
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Bibliographic record
Abstract
Abstract In this paper we investigate the intersections of classes of covering arrays (CAs) and packing arrays (PAs). The arrays appearing in these intersections obey to upper and lower bounds regarding the appearance of tuples in sub‐matrices—we call these arrays balanced covering arrays . We formulate and formalize first observations for which upper and lower bounds on the appearance of tuples it is of interest to consider these intersections of CAs and PAs. Outside of these bounds the intersections will be either empty, for the case of too restrictive constraints, or equal to the maximum element in the emerging lattices, for the case of too weak constraints. We present a column extension algorithm for classification of nonequivalent balanced CAs that uses a SAT solver or a pseudo‐Boolean (PB) solver to compute the columns suitable for array extension together with a lex‐leader ordering to identify unique representatives for each equivalence class of balanced CAs. These computations bring to light a dissection of classes of CAs that is partially nested due to the nature of the considered intersections. These dissections can be trivial, containing only a single type of balanced CAs, or can also appear as highly structured containing multiple nested types of balanced CAs. Our results indicate that balanced CAs are an interesting class of designs that is rich of structure.
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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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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