Delta-Complete Reachability Analysis (Part I)

We give a new framework for safety verification of nonlinear hybrid systems, based on deltadecidability of first-order logic formulas over the real numbers. We use expressive logic formulas (which can contain nonlinear ODEs with no analytic solutions) to encode bounded model checking and invariant-based reasoning. Based on the encoding, we solve bounded reachability and invariant validation problems using delta-complete decision procedures. Such techniques allow us to take into account of robustness properties of a system under delta-bounded numerical perturbations. This report describes Part I of the work, focusing on basic definitions and bounded reachability problems. This research was sponsored by the National Science Foundation grants no. CNS1330014, no. CNS0926181 and no. CNS0931985, the GSRC under contract no. 1041377, the Semiconductor Research Corporation under contract no. 2005TJ1366, and the Office of Naval Research under award no. N000141010188.