While Hamilton-Jacobi reachability analysis is a powerful tool for quantifying safety criticality and computing adversarial disturbances, it does have some limitations. One potential limitation is the computational complexity associated with solving the Hamilton-Jacobi equations, especially in high-dimensional state spaces. To address this, approximate solutions or sampling-based methods can be explored to make the computation more tractable. Another limitation is the assumption of perfect knowledge of the system dynamics, which may not always hold in real-world scenarios. Alternative approaches, such as model-free reinforcement learning methods or data-driven techniques, can be considered to learn the disturbance directly from data without relying on explicit dynamics models. By combining these approaches with Hamilton-Jacobi reachability analysis, a more robust and practical framework for computing adversarial disturbances can be developed.