On Using Time Without Clocks via Zigzag Causality

Even in the absence of clocks, time bounds on the duration of actions enable the use of time fordistributed coordination. This paper initiates an investigation of coordination in such a setting. A newcommunication structure called a zigzag pattern is introduced, and shown to guarantee bounds on therelative timing of events in this clockless model. Indeed, zigzag patterns are shown to be necessary andsufficient for establishing that events occur in a manner that satisfies prescribed bounds. We capturewhen a process can know that an appropriate zigzag pattern exists, and use this to provide necessary andsufficient conditions for timed coordination of events using a full-information protocol in the clocklessmodel.