  Falsification of hybrid systems is attracting ever-growing attention in
quality assurance of Cyber-Physical Systems (CPS) as a practical alternative to
exhaustive formal verification. In falsification, one searches for a falsifying
input that drives a given black-box model to output an undesired signal. In
this paper, we identify input constraints---such as the constraint "the
throttle and brake pedals should not pressed simultaneously" for an automotive
powertrain model---as a key factor for the practical value of falsification
methods. We propose three approaches for systematically addressing input
constraints in optimization-based falsification, two among which come from the
lexicographic method studied in the context of constrained multi-objective
optimization. Our experiments show the approaches' effectiveness.
