# On Using Time Without Clocks via Zigzag Causality

## TL;DR

This paper explores how to coordinate events in distributed systems without clocks by using a novel zigzag communication pattern to establish timing bounds, enabling effective synchronization without explicit time references.

## Contribution

It introduces the zigzag pattern as a new communication structure that guarantees and characterizes timing bounds in clockless distributed coordination.

## Key findings

- Zigzag patterns are necessary and sufficient for timing bounds.
- Conditions for process knowledge of zigzag patterns are established.
- Provides a full characterization of timed coordination without clocks.

## Abstract

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.