Optimization-based falsification employs stochastic optimization algorithms
to search for error input of hybrid systems. In this paper we introduce a
simple idea to enhance falsification, namely time staging, that allows the
time-causal structure of time-dependent signals to be exploited by the
optimizers. Time staging consists of running a falsification solver multiple
times, from one interval to another, incrementally constructing an input signal
candidate. Our experiments show that time staging can dramatically increase
performance in some realistic examples. We also present theoretical results
that suggest the kinds of models and specifications for which time staging is
likely to be effective