Formula Caching in DPLL
Bibliographic record
Abstract
We consider extensions of the DPLL approach to satisfiability testing that add a version ofmemoization, in which formulas that the algorithm has previously shown to be unsatisfiable are remembered for later use. Suchformula cachingalgorithms have been suggested for satisfiability and stochastic satisfiability by several authors. We formalize these methods by developing extensions of the fruitful connection that has previously been developed between DPLL algorithms for satisfiability and tree-like resolution proofs of unsatisfiability. We analyze a number of variants of these formula caching methods and characterize their strength in terms of proof systems. These proof systems are new and simple, and have a rich structure. We compare them to several studied proof systems: tree-like resolution, regular resolution, general resolution, Res(k), and Frege systems and present both simulation and separations. One of our most interesting results is the introduction of a natural and implementable form of DPLL with caching, FCWreason. This system is surprisingly powerful: we prove that it can polynomially simulate regular resolution, and furthermore, it can produce short proofs of some formulas that require exponential-size resolution proofs.
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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 | 0.021 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.009 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 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".