Constraint Satisfaction Problems and Their Reduction to Directed Graphs
Bibliographic record
Abstract
Constraint satisfaction problems present a general framework for studying a large class of algorithmic problems such as satisfaction of Boolean formulas, solving systems of equations over finite fields, graph colourings, as well as various applied problems in artificial intelligence (scheduling, allocation of cell phone frequencies, among others.) CSP (Constraint Satisfaction Problems) bring together graph theory, complexity theory and universal algebra. It is a well known result, due to Feder and Vardi, that any constraint satisfaction problem over a finite relational structure can be reduced to the homomorphism problem for a finite oriented graph. Until recently, it was not known whether this reduction preserves the type of the algorithm which solves the original constraint satisfaction problem, so that the same algorithm solves the corresponding digraph homomorphism problem. We look at how a recent construction due to Bulin, Deli´c, Jackson, and Niven can be used to show that the polynomial solvability of a constraint satisfaction problem using Datalog, a programming language which is a weaker version of Prolog, translates from arbitrary relational structures to digraphs.
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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 | 0.002 | 0.008 |
| 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 | 0.003 | 0.004 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.005 |
| Insufficient payload (model declined to judge) | 0.007 | 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".