AlphaSMT: A Reinforcement Learning Guided SMT Solver
Bibliographic record
Abstract
Satisfiability Modulo Theories (SMT) solvers are programs that decide whether a first-order logic formula is satisfiable. Over the last two decades, these solvers have become central to many methods and tools in fields as diverse as software engineering, verification, security, and Artificial Intelligence. Most modern SMT solvers provide user-controllable strategies, i.e., users can define a strategy that customizes a solving algorithm for their own problems by combining individual tactics as building blocks. A tactic is a well-defined and implemented reasoning step provided by the SMT solver, which either simplifies, trans- \nforms, or solves the given input SMT formula. The flexibility of customizing a strategy to a specialized type of formula is important since no existing strategy is considered optimal for all instances. However, finding a good customized strategy is challenging even for experts. \n \nIn this thesis we present a novel class of reinforcement-learning (RL) guided methods, implemented in the Z3 SMT solver and that we refer to as AlphaSMT, which adaptively constructs the expected best strategy for any given input SMT formula. Briefly, the AlphaSMT RL framework combines deep Monte-Carlo Tree Search (MCTS) and logical reasoning in a unique way in order to enable the RL agent to learn the best combination of tactics for a given class of formulas. In more detail, a deep neural network serves as both the value function and the policy, evaluating state-action pairs and making the decision of which \ntactic to choose at each step. The neural network is trained toward the optimal policy by learning from self-exploring sampling solving processes. MCTS is used as a lookahead planning step for each decision made in the sampling processes. \n \nWe evaluated the performance of AlphaSMT on benchmark sets from three SMT logics, namely, quantifier-free non-linear real arithmetic (QF NRA), quantifier-free non-linear integer arithmetic (QF NIA), and quantifier-free bit-vector (QF BV). In all these logics, AlphaSMT outperforms its base solver, Z3, by solving up to 80.5% more instances in a testing set. Evaluation results also show that a reasonably longer tactic timeout helps solve more instances and a pre-solver contributes significantly to the speedup.
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How this classification was reachedexpand
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 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".