Understanding Random SAT: Beyond the Clauses-to-Variables Ratio
Bibliographic record
Abstract
Abstract. It is well known that the ratio of the number of clauses to the numberof variables in a random k-SAT instance is highly correlated with the instance'sempirical hardness. We consider the problem of identifying such features of random SAT instances automatically using machine learning. We describe and ana-lyze models for three SAT solvers--kcnfs, oksolver and satz--and for two different distributions of instances: uniform random 3-SAT with varying ratio ofclauses-to-variables, and uniform random 3-SAT with fixed ratio of clauses-tovariables. We show that surprisingly accurate models can be built in all cases.Furthermore, we analyze these models to determine which features are most useful in predicting whether an instance will be hard to solve. Finally we discuss theuse of our models to build SATzilla, an algorithm portfolio for SAT.3 1 Introduction SAT is among the most studied problems in computer science, representing a genericconstraint satisfaction problem with binary variables and arbitrary constraints. It is also the prototypical N P-hard problem, and its worst-case complexity has received muchattention. Accordingly, it is not surprising that SAT has become a primary platform for the investigation of average-case and empirical complexity. Particular interest hasbeen paid to randomly generated SAT instances. In this paper we concentrate on such instances as they offer both a range of very easy to very hard instances for any giveninput size and the opportunity to make connections to a wealth of existing work.
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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 | 0.040 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.004 | 0.011 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.006 | 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".