We present a simulation-based approach for generating barrier certificate functions for safety verification of cyber-physical systems (CPS) that contain neural network-based controllers. A linear programming solver is utilized to find a candidate generator function from a set of simulation traces obtained by randomly selecting initial states for the CPS model. A level set of the generator function is then selected to act as a barrier certificate for the system, meaning it demonstrates that no unsafe system states are reachable from a given set of initial states. The barrier certificate properties are verified with an SMT solver. This approach is demonstrated on a case study in which a Dubins car model of an autonomous vehicle is controlled by a neural network to follow a given path.

One of the main challenges in testing autonomous driving systems is the presence of machine learning components, such as neural networks, for which formal properties are difficult to establish. We present a simulation-based testing framework that supports methods used to evaluate cyber-physical systems, such as test case generation and automatic falsification. We demonstrate how the framework can be used to evaluate closed-loop properties of autonomous driving system models that include machine learning components.

Many organizations are developing autonomous driving systems, which are expected to be deployed at a large scale in the near future. Despite this, there is a lack of agreement on appropriate methods to test, debug, and certify the performance of these systems. One of the main challenges is that many autonomous driving systems have machine learning (ML) components, such as deep neural networks, for which formal properties are difficult to characterize. We present a testing framework that is compatible with test case generation and automatic falsification methods, which are used to evaluate cyber-physical systems. We demonstrate how the framework can be used to evaluate closed-loop properties of an autonomous driving system model that includes the ML components, all within a virtual environment. We demonstrate how to use test case generation methods, such as covering arrays, as well as requirement falsification methods to automatically identify problematic test scenarios. The resulting framework can be used to increase the reliability of autonomous driving systems.

We provide a dynamic programming algorithm for the monitoring of a fragment of Timed Propositional Temporal Logic (TPTL) specifications. This fragment of TPTL, which is more expressive than Metric Temporal Logic, is characterized by independent time variables which enable the elicitation of complex real-time requirements. For this fragment, we provide an efficient polynomial time algorithm for off-line monitoring of finite traces. Finally, we provide experimental results on a prototype implementation of our tool in order to demonstrate the feasibility of using our tool in practical applications.