  In this paper we present a novel model checking approach to finite-time
safety verification of black-box continuous-time dynamical systems within the
framework of probably approximately correct (PAC) learning. The black-box
dynamical systems are the ones, for which no model is given but whose states
changing continuously through time within a finite time interval can be
observed at some discrete time instants for a given input. The new model
checking approach is termed as PAC model checking due to incorporation of
learned models with correctness guarantees expressed using the terms error
probability and confidence. Based on the error probability and confidence
level, our approach provides statistically formal guarantees that the
time-evolving trajectories of the black-box dynamical system over finite time
horizons fall within the range of the learned model plus a bounded interval,
contributing to insights on the reachability of the black-box system and thus
on the satisfiability of its safety requirements. The learned model together
with the bounded interval is obtained by scenario optimization, which boils
down to a linear programming problem. Three examples demonstrate the
performance of our approach.

Systems and Control;Formal Languages and Automata Theory;Systems and Control