Relativized Codes, Finite Decodability, and Bounded Languages
Bibliographic record
Abstract
A language C is a code relative to L if every word in L has a unique factorization into words of C; this is a generalization of a code. We extend this notion to d-decodability (respectively, finite-decodability) for $$d \ge 1$$ , which means that every word in L has at most d (respectively, a finite number of) factorizations into words of C. We study decidability of testing this property on languages accepted (respectively, generated) by different machine (respectively, grammar) models. Then, we study applications of finite decodability towards a new notion regarding bounded languages called C-boundedness for a language C, leading to several new and general decidability results. In particular, we show that in any family with a decidable finiteness problem that is effectively closed under homomorphism, inverse homomorphism, and intersection with regular languages, it is decidable, given a language L in the family and a set $$\varSigma ^{\le l}$$ of all strings of length at most l over $$\varSigma $$ , whether there exist words $$w_1, \ldots , w_n$$ in $$\varSigma ^{\le l}$$ such that $$L \subseteq w_1^* \cdots w_n^*$$ . This can be considered as a finite analog of the boundedness problem. This also implies that the letter-boundedness problem is always decidable in these families.
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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 | 0.001 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.002 | 0.009 |
| Scholarly communication | 0.004 | 0.009 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.006 |
| Insufficient payload (model declined to judge) | 0.005 | 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".