On the possibility and impossibility of achieving clock synchronization

It is known that clock synchronization can be achieved in the presence of faulty processors as long as the nonfaulty processors are connected, provided that some authentication technique is used. Without authentication the number of faults that can be tolerated has been an open question. Here we show that if we restrict logical clocks to running within some linear functions of real time, then clock synchronization is impossible without authentication when one-third or more of the processors are faulty. We also provide a lower bound on the closeness to which simultaneity can be achieved in the network as a function of the transmission and processing delay properties of the network.