On the Regularity of Iterated Hairpin Completion of a Single Word
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Bibliographic record
Abstract
Hairpin completion is an abstract operation modeling a DNA bio-operation which receives as input a DNA strand w = xαy\bar{α}, and outputs w' = xαy\bar{α}\bar{x}, where \bar{x} denotes the Watson-Crick complement of x. In this paper, we focus on the problem of finding conditions under which the iterated hairpin completion of a given word is regular. According to the numbers of words α and \bar{α} that initiate hairpin completion and how they are scattered, we classify the set of all words w. For some basic classes of words w containing small numbers of occurrences of α and \bar{α}, we prove that the iterated hairpin completion of w is regular. For other classes with higher numbers of occurrences of α and \bar{α}, we prove a necessary and sufficient condition for the iterated hairpin completion of a word in these classes to be regular.
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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 | 0.000 |
| 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