Bibliographic record
Abstract
A (non-circular) de Bruijn sequence w of order n is a word such that every word of length n appears exactly once in w as a factor. In this paper, we generalize the concept to different settings: the multi-shift de Bruijn sequence and the pseudo de Bruijn sequence. An m-shift de Bruijn sequence of order n is a word such that every word of length n appears exactly once in w as a factor that starts at a position im + 1 for some integer i ≥ 0. A pseudo de Bruijn sequence of order n with respect to an antimorphic involution θ is a word such that for every word u of length n the total number of appearances of u and θ(u) as a factor is one. We show that the number of m-shift de Bruijn sequences of order n is a n !a (m-n)(a n -1) for 1 ≤ n ≤ m and is (a m !) a n-m for 1 ≤ m ≤ n, where a is the size of the alphabet. We provide two algorithms for generating a multi-shift de Bruijn sequence. The multi-shift de Bruijn sequence is important for solving the Frobenius problem in a free monoid. We show that the existence of pseudo de Bruijn sequences depends on the given alphabet and antimorphic involution, and obtain formulas for the number of such sequences in some particular settings.
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How this classification was reachedexpand
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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.004 |
| Open science | 0.003 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".