Linear arithmetic satisfiability via strategy improvement
Bibliographic record
Abstract
Satisfiability-checking of formulas in the theory of linear rational arithmetic (LRA) has broad applications including program verification and synthesis. Satisfiability Modulo Theories (SMT) solvers are effective at checking satisfiability of the ground fragment of LRA, but applying them to quantified formulas requires a costly quantifier elimination step. This article presents a novel decision procedure for LRA that leverages SMT solvers for the ground fragment of LRA, but avoids explicit quantifier elimination. The intuition behind the algorithm stems from an interpretation of a quantified formula as a game between two players, whose goals are to prove that the formula is either satisfiable or not. The algorithm synthesizes a winning strategy for one of the players by iteratively improving candidate strategies for both. Experimental results demonstrate that the proposed procedure is competitive with existing solvers.
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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 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".