Expressibility Of Constraint Satisfaction Problems In Extensions Of First-Order Logic
Bibliographic record
Abstract
<p>A fundamental open problem in finite model theory and, specifically, descriptive complexity is the question whether there exists a logic which characterizes solvability of algorithmic decision polynomial time on the class of finite relational structures. A prominent candidate is the logic of Choiceless Polynomial Time (CPT) (optionally counting), a strict extension of the first-order logic. The expressibility problem for properties of finite relational structures in CPT (or CPT+C) is intrinsically hard, but CPT can be replaced by a more standard model-theoretic construction.</p> <p>We show that constraint satisfaction problems over Maltsev templates can be expressed in the logic PIL+H. Furthermore, we show that the algorithm for Maltsev templates also solves said instances of constraint satisfaction problems over finite, idempotent Taylor algebras. This proves that for every finite, idempotent algebra A, the problem CSP(A) is either NP-complete or its solvability can be defined in the logic PIL+H.</p>
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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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.002 |
| 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".