Satisfiability Modulo ODEs

We study SMT problems over the reals containing ordinary differential equations. They are important for formal verification of realistic hybrid systems and embedded software. We develop delta-complete algorithms for SMT formulas that are purely existentially quantified, as well as exists-forall formulas whose universal quantification is restricted to the time variables. We demonstrate scalability of the algorithms, as implemented in our open-source solver dReal, on SMT benchmarks with several hundred nonlinear ODEs and variables.