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The paper extends the recent star reachability method to verify the robustness of recurrent neural networks (RNNs) for use in safety-critical applications. RNNs are a popular machine learning method for various applications, but they are vulnerable to adversarial attacks, where slightly perturbing the input sequence can lead to an unexpected result. Recent notable techniques for verifying RNNs include unrolling, and invariant inference approaches. The first method has scaling issues since unrolling an RNN creates a large feedforward neural network. The second method, using invariant sets, has better scalability but can produce unknown results due to the accumulation of overapproximation errors over time. This paper introduces a complementary verification method for RNNs that is both sound and complete. A relaxation parameter can be used to convert the method into a fast overapproximation method that still provides soundness guarantees. The method is designed to be used with NNV, a tool for verifying deep neural networks and learning-enabled cyber-physical systems. Compared to state-of-the-art methods, the extended exact reachability method is 10 × faster, and the overapproximation method is 100 × to 5000 × faster. 

Perception algorithms in autonomous vehicles are vital for the vehicle to understand the semantics of its surroundings, including detection and tracking of objects in the environment. The outputs of these algorithms are in turn used for decision-making in safety-critical scenarios like collision avoidance, and automated emergency braking. Thus, it is crucial to monitor such perception systems at runtime. However, due to the high-level, complex representations of the outputs of perception systems, it is a challenge to test and verify these systems, especially at runtime. In this paper, we present a runtime monitoring tool, PerceMon that can monitor arbitrary specifications in Timed Quality Temporal Logic (TQTL) and its extensions with spatial operators. We integrate the tool with the CARLA autonomous vehicle simulation environment and the ROS middleware platform while monitoring properties on state-of-the-art object detection and tracking algorithms.