Guiding High-Performance SAT Solvers with Unsat-Core Predictions (1903.04671v7)

Abstract: The NeuroSAT neural network architecture was recently introduced for predicting properties of propositional formulae. When trained to predict the satisfiability of toy problems, it was shown to find solutions and unsatisfiable cores on its own. However, the authors saw "no obvious path" to using the architecture to improve the state-of-the-art. In this work, we train a simplified NeuroSAT architecture to directly predict the unsatisfiable cores of real problems. We modify several high-performance SAT solvers to periodically replace their variable activity scores with NeuroSAT's prediction of how likely the variables are to appear in an unsatisfiable core. The modified MiniSat solves 10% more problems on SAT-COMP 2018 within the standard 5,000 second timeout than the original does. The modified Glucose solves 11% more problems than the original, while the modified Z3 solves 6% more. The gains are even greater when the training is specialized for a specific distribution of problems; on a benchmark of hard problems from a scheduling domain, the modified Glucose solves 20% more problems than the original does within a one-hour timeout. Our results demonstrate that NeuroSAT can provide effective guidance to high-performance SAT solvers on real problems.

• The paper introduces NeuroCore, a simplified NeuroSAT model that predicts unsat cores to guide variable selection in SAT solvers.
• The approach leverages training on over 150,000 generated unsat subproblems, achieving a 10% boost on SATCOMP-2018 benchmarks.
• Integrating unsat-core predictions into solvers like MiniSat, Glucose, and Z3 bridges neural guidance with traditional heuristics for complex problems.

An Essay on "Guiding High-Performance SAT Solvers with Unsat-Core Predictions"

The paper "Guiding High-Performance SAT Solvers with Unsat-Core Predictions" by Daniel Selsam and Nikolaj Bjørner introduces a promising integration of neural networks with state-of-the-art SAT solvers. The authors build upon the NeuroSAT neural network architecture, aiming to enhance the performance of SAT solvers by guiding them using predictions about unsatisfiable cores. This approach contrasts with earlier ambitions of NeuroSAT, which focused on small, constrained problems without a direct path to improving SAT solvers on more intricate, real-world problems.

Methodology and Results

The authors propose training a simplified version of NeuroSAT, termed NeuroCore, to predict unsatisfiable cores of real problems. The innovation here lies in utilizing the neural network to inform the decision-making process within SAT solvers such as MiniSat, Glucose, and Z3. These solvers were modified to replace conventional variable activity scores with predictions from NeuroCore, effectively 'refocusing' the solver towards more promising search regions. The empirical results reveal that these modified solvers exhibit improved efficacy in tackling SATCOMP-2018 benchmarks—NeuroCore-assisted MiniSat solved 10% more problems than its unaltered counterpart.

A significant methodological component is data generation for NeuroCore's training. Given the scarcity of labeled unsatisfiable problems, the authors developed a means to construct over 150,000 training examples by generating unsatisfiable subproblems from existing benchmarks. The trained NeuroCore was then integrated into MiniSat, Glucose, and Z3 to periodically adjust their decision heuristics based on unsat-core predictions.

The efficacy of this integration was highlighted in various experiments. When applied to SATCOMP-2018, MiniSat's performance improved by solving 205 problems compared to 187 by the original solver, underscoring a 10% enhancement. Likewise, Glucose and Z3 also exhibited marked improvements. Particularly, when NeuroCore was tailored to a specific distribution of hard scheduling problems, an impressive 20% increase in problem-solving capability was recorded for the Glucose solver.

Practical and Theoretical Implications

The results from this paper suggest a significant leap in integrating machine learning with discrete search problems. It not only enhances the practicability of NeuroSAT in real-world applications but also opens new pathways for hybrid solver design. This integrated approach allows some of the traditional boundaries of SAT solvers to be revisited and potentially redefined, bridging the gap between machine learning-derived insights and classical search heuristics.

From a theoretical standpoint, this work proposes a novel way to leverage data-driven predictions without fully substituting trusted heuristics like EVSIDS. Despite its primary focus on unsat core predictions, the paper highlights the potential benefits of exploring machine learning applications in other SAT problem areas, such as learning variable activity directly from clause activity and not just relying on historical score derivatives.

Future Directions

Future research should explore this integration further, especially considering alternative training regimes that might be adaptive to specific problem domains. The use of different neural architectures or hyperparameter configurations in learning phase selection, heuristic refinement in clause deletion, or even in proof compression can be promising avenues. Additionally, further refinement might include focusing on generalizing to a variety of SAT problem types and incorporating unsupervised or reinforcement learning strategies to reduce the dependency on extensive labeled data.

The implications of NeuroSAT-guided solvers extend beyond SAT to potential crossover benefits in related computational problem spaces. This paper sets a precedent for employing neural guidance in such contexts, arguably heralding a new era where hybrid computing solutions become the benchmark in tackling complex, large-scale combinatorial problems.