Bibliographic record
Abstract
Although bimachines are not widely used in practice, they represent a central concept in the study of rational functions. Indeed, they are finite state machines specifically designed to implement rational word functions. Their modelling power is equal to that of single-valued finite transducers. From the theoretical point of View, bimachines reflect the decomposition of a rational function into a left and a right sequential function. In this paper we define three new types of bimachines, classified according to the scanning direction of their reading heads. Then we prove that these types of bimachines are equivalent to the classical one and for doing so, we define and use a new concept, of structurally-reversed automaton. Consequently, we prove that the scanning directions of bimachines are irrelevant from the point of view of their modelling power. This leads to a method of simulating a bimachine by a left sequential transducer (or generalized sequential machines -- GSM for short). Indeed, a preprocessing of the input word al- lows sequential transducers to realize the full range of rational functions. Remarkably enough, we basically show that the so versatile functional transducers - nondeterminis- tic and with $\lambda$-input transitions - can successfully be replaced by a simple deterministic setup: a "trimmer" coupled with a GSM. Intuitively, this fact proves that sequential functions are not much weaker than rational functions.
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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 | 0.000 | 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 | 0.003 |
| Open science | 0.001 | 0.001 |
| 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".