Bibliographic record
Abstract
The constraint satisfaction problem (CSP) involves deciding, given a set of variables and a set of constraints on the variables, whether or not there is an assignment to the variables satisfying all of the constraints. One formulation of the CSP is as the problem of deciding, given a pair (G ℍ) of relational structures, whether or not there is a homomorphism from the first structure to the second structure. The CSP is generally NP-hard; a common way to restrict this problem is to fix the second structure ℍ so that each structure ℍ gives rise to a problem CSP(ℍ). The problem family CSP(ℍ) has been studied using an algebraic approach, which links the algorithmic and complexity properties of each problem CSP(ℍ) to a set of operations, the so-called polymorphisms of ℍ. Certain types of polymorphisms are known to imply the polynomial-time tractability of CSP(ℍ), and others are conjectured to do so. This article systematically studies—for various classes of polymorphisms—the computational complexity of deciding whether or not a given structure ℍ admits a polymorphism from the class. Among other results, we prove the NP-completeness of deciding a condition conjectured to characterize the tractable problems CSP(ℍ), as well as the NP-completeness of deciding if CSP(ℍ) has bounded width.
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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 | 0.010 | 0.095 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.004 |
| Bibliometrics | 0.002 | 0.004 |
| Science and technology studies | 0.003 | 0.008 |
| Scholarly communication | 0.007 | 0.028 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.005 | 0.014 |
| Insufficient payload (model declined to judge) | 0.012 | 0.002 |
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".