Bibliographic record
Abstract
Constraint satisfaction problems (CSPs) are one of the central topics in theoretical computer science, in particular, in the area of artificial intelligence. Their computational complexity is due to relatively recent results from areas of mathematics, including finite-model-theory, algebra and graph homomorphisms. The main conjecture by Feder and Vardi states that any CSP over a finite relational template is either in P or is NP-complete. Further, it amounts to showing that every non NP-complete CSP can be expressed as an extension of first-order logic. A finite template is Mal'tsev, a compatible algebraic operation, which is closely related to an affine space over a finite field. The so-called Bulatov-Dalmau algorithm, a natural generalization of the Gaussian elimination on vector spaces, shows such CSPs are tractable. In this work, we prove that CSPs described over a finite template Mal'tsev are expressible in logic LFP+rnk, providing a logical proof that such CSPs are tractable.
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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 | 0.001 | 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 | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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".