We develop algorithms for computing Craig interpolants for first-order formulas over real numbers with a wide range of nonlinear functions, including transcendental functions and differential equations. We transform proof traces from δ-complete decision procedures into interpolants that consist of Boolean combinations of linear constraints. The algorithms are guaranteed to find the interpolants between two formulas A and B whenever A ∧ B is not δ-satisfiable. At the same time, by exploiting δ-perturbations one can parameterize the algorithm to find interpolants with different positions between A and B. We show applications of the methods in control and robotic design, and hybrid system verification.
CITATION STYLE
Gao, S., & Zufferey, D. (2016). Interpolants in nonlinear theories over the reals. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9636, pp. 625–641). Springer Verlag. https://doi.org/10.1007/978-3-662-49674-9_41
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