Satisfiability Modulo Theories

SMT combines Boolean reasoning with specialized theory solvers to decide whether constraints can hold together, supporting applications such as software and neural-network verification, scheduling, and synthesis. A central approach is CDCL(T), which interleaves clause learning with theory checks; other methods use bit-blasting, optimization, or translations between SMT and constraint-programming or SAT solvers. Current work also explores proof-producing solvers and neuro-symbolic systems that use language models to propose constraints or lemmas which solvers can validate. A key tension is scaling to large or nonlinear problems while preserving exact, checkable guarantees.