Testing Autonomous Systems with Believed Equivalence Refinement

Continuous engineering of autonomous driving functions commonly requires deploying vehicles in road testing to obtain inputs that cause problematic decisions. Although the discovery leads to producing an improved system, it also challenges the foundation of testing using equivalence classes and the associated relative test coverage criterion. In this paper, we propose believed equivalence, where the establishment of an equivalence class is initially based on expert belief and is subject to a set of available test cases having a consistent valuation. Upon a newly encountered test case that breaks the consistency, one may need to refine the established categorization in order to split the originally believed equivalence into two. Finally, we focus on modules implemented using deep neural networks where every category partitions an input over the real domain. We establish new equivalence classes by guiding the new test cases following directions suggested by its k-nearest neighbors, complemented by local robustness testing. The concept is demonstrated in a lane-keeping assist module indicating the potential of our proposed approach.