Satisfiability (SAT) Solving with Learning is the augmentation of classical Boolean SAT solvers with machine learning heuristics — using GNNs or other models to predict variable assignments or branching decisions to speed up the solving of NP-complete problems.

What Is this field?

• SAT Solver: Finds if there exists an assignment of True/False to variables to make a formula True. (CDCL algorithm).
• Bottleneck: Choosing which variable to split on next (Branching Heuristic).
• ML Solution: Train a GNN on the formula's structure (variable-clause graph) to predict the best split.
• NeuroSAT: A famous architecture that learns to solve SAT problems end-to-end.

Why It Matters

• Combinatorial Optimization: Solving scheduling, routing, and verification problems faster.
• Generalization: A model trained on small 40-variable problems can often guide solvers on huge 4000-variable problems.

Satisfiability Solving with Learning is AI-guided search — using neural intuition to navigate the exponentially large search spaces of logic problems.