The coordination of a sequence of actions, to be performed in a linear temporal order in a distributed system, is studied. While in asynchronous message-passing systems such ordering of events requires the construction of message chains based on Lamport's happened-before relation, this is no longer true in the presence of time bounds on message delivery. Given such bounds, the mere passage of time can provide information about the occurrence of events at remote sites, without the need for explicit confirmation. A new causal structure called the centipede is introduced, and it is shown that centipedes must exist in every execution where linear ordering of actions is ensured. Centipedes capture the subtle interplay between the explicit information obtained via message chains, and the indirectly derived information gained by the passage of time, given the time bounds. Centipedes are defined using two relations. One is called syncausality, a slight generalisation of the happened-before relation. The other is a novel bound guarantee relation among events, that is based on the bounds on message transmission. In a precise sense, centipedes play a role in the synchronous setting analogous to that played by message chains in asynchronous systems. Our study is based on a knowledge-based analysis of distributed coordination. Temporally linear coordination is reduced to nested knowledge (knowledge about knowledge). Obtaining nested knowledge of a spontaneous event is, in turn, shown to require the existence of an appropriate centipede.

This paper studies the role that known bounds on message transmission times in a computer network play on the evolution of the epistemic state over time. A connection to cones of causal influence analogous to, and more general than, light cones is presented. Focusing on lower bounds on message transmission times, an analysis is presented of how knowledge about when others are guaranteed to be ignorant about an event of interest ("knowing that they don't know") can arise. This has implications in competitive settings, in which knowing about another's ignorance can provide an advantage.