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

Prioritizing Corners in OoD Detectors via Symbolic String Manipulation