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Future autonomous systems will employ sophisticated machine learning techniques for the sensing and perception of the surroundings and the making corresponding decisions for planning, control, and other actions. They often operate in highly dynamic, uncertain and challenging environment, and need to meet stringent timing, resource, and mission requirements. In particular, it is critical and yet very challenging to ensure the safety of these autonomous systems, given the uncertainties of the system inputs, the constant disturbances on the system operations, and the lack of analyzability for many machine learning methods (particularly those based on neural networks). In this paper, we will discuss some of these challenges, and present our work in developing automated, quantitative, and formalized methods and tools for ensuring the safety of autonomous systems in their design and during their runtime …