  Autonomous systems with machine learning-based perception can exhibit
unpredictable behaviors that are difficult to quantify, let alone verify. Such
behaviors are convenient to capture in probabilistic models, but probabilistic
model checking of such models is difficult to scale -- largely due to the
non-determinism added to models as a prerequisite for provable conservatism.
Statistical model checking (SMC) has been proposed to address the scalability
issue. However it requires large amounts of data to account for the
aforementioned non-determinism, which in turn limits its scalability. This work
introduces a general technique for reduction of non-determinism based on
assumptions of "monotonic safety'", which define a partial order between system
states in terms of their probabilities of being safe. We exploit these
assumptions to remove non-determinism from controller/plant models to
drastically speed up probabilistic model checking and statistical model
checking while providing provably conservative estimates as long as the safety
is indeed monotonic. Our experiments demonstrate model-checking speed-ups of an
order of magnitude while maintaining acceptable accuracy and require much less
data for accurate estimates when running SMC -- even when monotonic safety does
not perfectly hold and provable conservatism is not achieved.
