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 for distributed coordination. This paper initiates an investigation of coordination in such a setting. A new communication structure called a zigzag pattern is introduced, and shown to guarantee bounds on the relative timing of events in this clockless model. Indeed, zigzag patterns are shown to be necessary and sufficient for establishing that events occur in a manner that satisfies prescribed bounds. We capture when a process can know that an appropriate zigzag pattern exists, and use this to provide necessary and sufficient conditions for timed coordination of events using a full-information protocol in the clockless model.