  For safety assurance of deep neural networks (DNNs), out-of-distribution
(OoD) monitoring techniques are essential as they filter spurious input that is
distant from the training dataset. This paper studies the problem of
systematically testing OoD monitors to avoid cases where an input data point is
tested as in-distribution by the monitor, but the DNN produces spurious output
predictions. We consider the definition of "in-distribution" characterized in
the feature space by a union of hyperrectangles learned from the training
dataset. Thus the testing is reduced to finding corners in hyperrectangles
distant from the available training data in the feature space. Concretely, we
encode the abstract location of every data point as a finite-length binary
string, and the union of all binary strings is stored compactly using binary
decision diagrams (BDDs). We demonstrate how to use BDDs to symbolically
extract corners distant from all data points within the training set. Apart
from test case generation, we explain how to use the proposed corners to
fine-tune the DNN to ensure that it does not predict overly confidently. The
result is evaluated over examples such as number and traffic sign recognition.
