Expressiveness and complexity of order dependencies
Bibliographic record
Abstract
Dependencies play an important role in databases. We study order dependencies (ODs)--and unidirectional order dependencies (UODs), a proper sub-class of ODs--which describe the relationships among lexicographical orderings of sets of tuples. We consider lexicographical ordering, as by the order-by operator in SQL, because this is the notion of order used in SQL and within query optimization. Our main goal is to investigate the inference problem for ODs, both in theory and in practice. We show the usefulness of ODs in query optimization. We establish the following theoretical results: (i) a hierarchy of order dependency classes; (ii) a proof of co-NP-completeness of the inference problem for the subclass of UODs (and ODs); (iii) a proof of co-NP-completeness of the inference problem of functional dependencies (FDs) from ODs in general, but demonstrate linear time complexity for the inference of FDs from UODs; (iv) a sound and complete elimination procedure for inference over ODs; and (v) a sound and complete polynomial inference algorithm for sets of UODs over restricted domains.
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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 | 0.004 | 0.026 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.006 | 0.014 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.004 | 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 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".