Linear arithmetic satisfiability via strategy improvement
Why this work is in the frame
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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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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 it