Zero-Avoiding Transducers, Length Separable Relations, and the Rational Asymmetric Partition Problem
Bibliographic record
Abstract
We consider the problem of partitioning effectively a given irreflexive (and possibly symmetric) rational relation [Formula: see text] into two asymmetric rational relations. This problem is motivated by a recent method of embedding an [Formula: see text]-independent language into one that is maximal [Formula: see text]-independent, where the method requires to use an asymmetric partition of [Formula: see text]. We solve the problem when [Formula: see text] is length-separable, which means that the following two subsets of [Formula: see text] are rational: the subset of word pairs [Formula: see text] where [Formula: see text]; and the subset of word pairs [Formula: see text] where [Formula: see text]. This property is satisfied by all recognizable, all left synchronous, and all right synchronous relations. We leave it as an open problem when [Formula: see text] is not length-separable. We also define zero-avoiding transducers for length-separable relations, which makes our partitioning solution constructive.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.002 |
| 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 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".