Satisfiability and Algorithms for Non-uniform Random k-SAT
Bibliographic record
Abstract
Solving Satisfiability is at the core of a wide range of applications from Knowledge Representation to Logic Programming to Software and Hardware Verification. One of the models of Satisfiability, the Random Satisfiability problem, has received much attention in the literature both, as a useful benchmark for SAT solvers, and as an exciting mathematical object. In this paper we tackle a somewhat nonstandard type of Random Satisfiability, the one where instances are not chosen uniformly from a certain class of instances, but rather from a certain nontrivial distribution. More precisely, we use so-called Configuration Model, in which we start with a distribution of degrees (the number of occurrences) of a variable, sample the degree of each variable and then generate a random instance with the prescribed degrees. It has been proposed previously that by properly selecting the starting distribution (to be, say, power law or lognorm) one can approximate at least some aspect of `industrial' instances of SAT. Here we suggest an algorithm that solves such problems for a wide range of degree distributions and obtain a necessary and a sufficient condition for the satisfiability of such formulas.
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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 | 0.005 | 0.032 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.003 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.003 | 0.007 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.009 | 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".