  In this letter, we detail our randomized approach to safety-critical system
verification. Our method requires limited system data to make a strong
verification statement. Specifically, our method first randomly samples initial
conditions and parameters for a controlled, continuous-time system and records
the ensuing state trajectory at discrete intervals. Then, we evaluate these
states under a candidate barrier function $h$ to determine the constraints for
a randomized linear program. The solution to this program then provides either
a probabilistic verification statement or a counterexample. To show the
validity of our results, we verify the robotarium simulator and identify
counterexamples for its hardware counterpart. We also provide numerical
evidence to validate our verification statements in the same setting.
Furthermore, we show that our method is system-independent by performing the
same verification method on a quadrupedal system in a multi-agent setting as
well.
