We present a simple, efficient, and unified solution to the problems of synchronizing, initializing, and integrating clocks for systems with different types of failures: crash, omission, and arbitrary failures with and without message authentication. This is the first known solution that achieves optimal accuracy-the accuracy of synchronized clocks (with respect to real time) is as good as that specified for the underlying hardware clocks. The solution is also optimal with respect to the number

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... of faulty processes that can be tolerated to achieve this accuracy.