The shape of reactive coordination tasks

This paper studies the interaction between knowledge, time and coordination in systems in which timing information is available. Necessary conditions are given for the causal structure in coordination problems consisting of orchestrat- ing a set of actions in a manner that satisfies a variety of temporal ordering assumptions. Results are obtained in two main steps: A specification of coordination is shown to re- quire epistemic properties, and the causal structure required to obtain these properties is characterised via \knowledge gain" theorems. A new causal structure called a centibroom structure is presented, generalising previous causal struc- tures for this model. It is shown to capture coordination tasks in which a sequence of clusters of events is performed in linear order, while within each cluster all actions must take place simultaneously. This form of coordination is shown to require the agents to gain a nested common knowledge of particular facts, which in turn requires a centibroom. Al- together, the results presented provide a broad view of the causal shape underlying partially ordered coordinated ac- tions. This, in turn, provides insight into and can enable the design of efficient solutions to the coordination tasks in question.