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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 δ-complete algorithms for SMT formulas that are purely existentially quantified, as well as ∃∀-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.
Gao et al. (2013) studied this question.