  The conformance testing problem for dynamical systems asks, given two
dynamical models (e.g., as Simulink diagrams), whether their behaviors are
"close" to each other. In the semi-formal approach to conformance testing, the
two systems are simulated on a large set of tests, and a metric, defined on
pairs of real-valued, real-timed trajectories, is used to determine a lower
bound on the distance. We show how the Skorkhod metric on continuous dynamical
systems can be used as the foundation for conformance testing of complex
dynamical models. The Skorokhod metric allows for both state value mismatches
and timing distortions, and is thus well suited for checking conformance
between idealized models of dynamical systems and their implementations. We
demonstrate the robustness of the system conformance quantification by proving
a \emph{transference theorem}: trajectories close under the Skorokhod metric
satisfy "close" logical properties. Specifically, we show the result for the
timed linear time logic \TLTL augmented with a rich class of temporal and
spatial constraint predicates. We provide a window-based streaming algorithm to
compute the Skorokhod metric, and use it as a basis for a conformance testing
tool for Simulink. We experimentally demonstrate the effectiveness of our tool
in finding discrepant behaviors on a set of control system benchmarks,
including an industrial challenge problem.
