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We consider several problems relating to strongly-connected directed networks of identical finite-state processors that work synchronously in discrete time steps. The conceptually simplest of these problems is the Wake Up and Report Problem; this is the problem of having a unique "root" processor send a signal to all other processors in the network and then enter a special "done" state only when all other processors have received the signal. The most difficult of the problems we consider is the classic Firing Squad Synchronization Problem; this is the much-studied problem of achieving macro-synchronization in a network given micro-synchronization. We show via a complex algorithmic application of the "snake" data structure first introduced in Even, Litman, and Winkler[6] that these two problems in particular are asymptotically time-equivalent up to a constant factor. This result leads immediately to the inclusion of several other related problems into this new asymptotic time-class.

The wake up and report problem is time-equivalent to the firing squad synchronization problem