Self-stabilizing clock synchronization with Byzantine faults

In a distributed system, it is often necessary to keep the logical clocks of theproceasors synchronized. In sucha system physical clocks may drift and messages may have varying delivery times. Moreover, processors may be faulty, and in many cases the type of failures is not pr~ dictable in advance. To handle this situation, the worst type of failures must be considered, namely Byzantine faults. In the presence of Byzantine faults a processor can exhibit arbitrary behavior, which can include “malicious” or “two-faced” behavior. The problem of keeping clocks synchronized in the presence of Byzantine faults was introduced by Lamport and MelliarSmith [LM85] and has been extensively studied since then. Many of the protocols for this problem assume that the clocks are initially synchronized and thus focus on keeping them synchronized in the presence of clock drift. The problem of how to ensure that the clocks are initially synchronized was addressed in some of the works. However, in these works, some mechanism is assumed that allows all the nonfaulty processors to begin the protocol within a bounded time period of each other. The mechanism essentially is that the processes are assumed to wake up in a distinguished initial state, in which they can uniquely perform initializing actions, including communication with each other.