# Complexity Theory of Solvers

Conflict-driven clause-learning (CDCL) SAT solvers, as well as satisfiability modulo theories (SMT) solvers, routinely solve formulas with thousands to millions of variables and clauses, despite the satisfiability problem being NP-complete. At the same time, small randomly generated formulas are difficult for the same solvers. The goal of this work is to understand which aspects of modern SAT/SMT solvers, as well as which measures of SAT/SMT formulas, relate best to solving performance.

Our line of work follows along 4 main lines of reasoning:

- Deriving proof complexity lower bounds to demonstrate the hardness of certain formulas for modern solvers;
- Deriving parameterized complexity upper bounds to demonstrate how certain measures of formulas relate to hardness;
- Characterizing SAT/SMT solvers through the lens of machine learning;
- Improving our understanding of encodings and reductions of formulas.