Combinations of active automata learning, model-based testing and model checking have been successfully used in numerous applications, e.g., for spotting bugs in implementations of major network protocols and to support refactoring of embedded controllers. However, in the large majority of these applications, model checking is only used at the very end, when no counterexample can be found anymore for the latest hypothesis model. This contrasts with the original proposal of black-box checking (BBC) by Peled, Vardi & Yannakakis, which applies model checking for all hypotheses, also the intermediate ones. In this article, we present the first systematic evaluation of the ability of BBC to find bugs quickly, based on 77 benchmark models from real protocol implementations and controllers for which specifications of safety properties are available. Our main finding are: (a) In cases where the full model can be learned, BBC detects violations of the specifications with just 3% of the queries needed by an approach in which model checking is only used for the full model. (b) Even when the full model cannot be learned, BBC is still able to detect many violations of the specification. In particular, BBC manages to detect 96% of the safety property violations in the challenging RERS 2019 industrial LTL benchmarks. (c) Our results also confirm that BBC is way more effective than existing model-based testing algorithms in finding deep bugs in implementations.

@inproceedings{paperbot12439,
  title = {Quick Bug Detection through Black-Box Checking},
  author = {Bram Pellen and María Belén Rodríguez and Frits Vaandrager and Petra van den Bos},
  booktitle = {ASE},
  year = {2026},
  doi = {10.1145/3832783.3834347}
}