Splitting on Demand in Satisfiability Modulo Theories

Опубликовано 7 сентября 2016, 16:41

Lazy algorithms for Satisfiability Modulo Theories (SMT) combine a generic DPLL-based SAT engine with a theory solver for a given theory T that can decide the T-consistency of conjunctions of ground literals. For many theories of interest, theory solvers need to reason by performing internal case splits. In this talk we argue that it is more convenient to delegate these case splits to the DPLL engine instead. The delegation can be done on demand for solvers that can encode their internal case splits into one or more clauses, possibly including new constants and literals. This results in drastically simpler theory solvers. We present this splitting-on-demand idea in an extension of Abstract DPLL Modulo Theories, a framework for modeling and reasoning about lazy algorithms for SMT. We also show that splitting-on-demand can be naturally refined to include efficient Nelson-Oppen-like combination of multiple theories and their solvers.