  We introduce the State Classification Problem (SCP) for hybrid systems, and
present Neural State Classification (NSC) as an efficient solution technique.
SCP generalizes the model checking problem as it entails classifying each state
$s$ of a hybrid automaton as either positive or negative, depending on whether
or not $s$ satisfies a given time-bounded reachability specification. This is
an interesting problem in its own right, which NSC solves using
machine-learning techniques, Deep Neural Networks in particular. State
classifiers produced by NSC tend to be very efficient (run in constant time and
space), but may be subject to classification errors. To quantify and mitigate
such errors, our approach comprises: i) techniques for certifying, with
statistical guarantees, that an NSC classifier meets given accuracy levels; ii)
tuning techniques, including a novel technique based on adversarial sampling,
that can virtually eliminate false negatives (positive states classified as
negative), thereby making the classifier more conservative. We have applied NSC
to six nonlinear hybrid system benchmarks, achieving an accuracy of 99.25% to
99.98%, and a false-negative rate of 0.0033 to 0, which we further reduced to
0.0015 to 0 after tuning the classifier. We believe that this level of accuracy
is acceptable in many practical applications, and that these results
demonstrate the promise of the NSC approach.
