Bibliographic record
Abstract
Sequences (L n | n ≥ k), called streams, of regular languages L n are considered, where k is some small positive integer, n is the state complexity of L n , and the languages in a stream differ only in the parameter n, but otherwise, have the same properties. The following measures of complexity are proposed for any stream: (1) the state complexity n of L n , that is, the number of left quotients of L n (used as a reference); (2) the state complexities of the left quotients of L n ; (3) the number of atoms of L n ; (4) the state complexities of the atoms of L n ; (5) the size of the syntactic semigroup of L n ; and the state complexities of the following operations: (6) the reverse of L n ; (7) the star of L n ; (8) union, intersection, difference and symmetric difference of L m and L n ; and (9) the concatenation of L m and L n . A stream that has the highest possible complexity with respect to these measures is then viewed as a most complex stream. The language stream (U n (a, b, c) | n ≥ 3) is defined by the deterministic finite automaton with state set {0, 1, … , n−1}, initial state 0, set {n−1} of final states, and input alphabet {a, b, c}, where a performs a cyclic permutation of the n states, b transposes states 0 and 1, and c maps state n − 1 to state 0. This stream achieves the highest possible complexities with the exception of boolean operations where m = n. In the latter case, one can use U n (a, b, c) and U n (b, a, c), where the roles of a and b are interchanged in the second language. In this sense, U n (a, b, c) is a universal witness. This witness and its extensions also apply to a large number of combined regular operations.
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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 | 0.002 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".