Bibliographic record
Abstract
To get a more comprehensive understanding of the amount of branching in computations of a nondeterministic finite automaton (NFA), we introduce and study the string path width and depth path width measures. For a given NFA, the string path width on a string [Formula: see text] counts the number of all complete computations on [Formula: see text], and the depth path width on an integer [Formula: see text] counts the number of complete computations on all strings of length [Formula: see text]. We give an algorithm to decide the finiteness of the depth path width of an NFA. Deciding finiteness of string path width can be reduced to the corresponding question on ambiguity. An NFA is nearly acyclic if any computation can pass through at most one cycle. The class of nearly acyclic NFAs consists of exactly all NFAs with finite depth path width. Using this characterization we show that the finite depth path width of an [Formula: see text]-state NFA over a [Formula: see text]-letter alphabet is at most [Formula: see text] and that this bound is tight. The nearly acyclic NFAs recognize exactly the class of constant density regular languages.
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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 | 0.001 | 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 | 0.001 | 0.003 |
| Open science | 0.002 | 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".