Falsification of Conditional Safety Properties for Cyber-Physical Systems with Gaussian Process Regression

We propose a framework to solve falsification problems of conditional safety properties—specifications such that “a safety property \(\varphi _{\mathsf {safe}}\) holds whenever an antecedent condition \(\varphi _{\mathsf {cond}}\) holds.” In the outline, our framework follows the existing one based on robust semantics and numerical optimization. That is, we search for a counterexample input by iterating the following procedure: (1) pick up an input; (2) test how robustly the specification is satisfied under the current input; and (3) pick up a new input again hopefully with a smaller robustness. In falsification of conditional safety properties, one of the problems of the existing algorithm is the following: we sometimes iteratively pick up inputs that do not satisfy the antecedent condition \(\varphi _{\mathsf {cond}}\), and the corresponding tests become less informative. To overcome this problem, we employ Gaussian process regression—one of the model estimation techniques—and estimate the region of the input search space in which the antecedent condition \(\varphi _{\mathsf {cond}}\) holds with high probability.