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Connected Automated Vehicles (CAVs) have drawn much attention in recent years. High reliable automatic technologies can help CAVs to follow given trajectories well. However, safety and efficiency are hard to be ensured since the interactions between CAVs and pedestrians are complex problems. Thus, this study focuses on cooperative intersection management for CAVs and pedestrians. To avoid the effects of uncertainty about pedestrian behaviors, an indirect way is to use pedestrians' signal lights to guide the movements of pedestrians, and such lights with communication devices can share information with CAVs to make decisions together. In time domains, a general conflict-free rule is established depending on the positions of CAVs and crosswalks. Geometric analysis with coordinate calculation is used to accurately determine the feasible vehicle trajectories and the reasonable periods for signal lights …