On quasi orders of words and the confluence property
Theoretical Computer Science
Time-varying graphs and dynamic networks
ADHOC-NOW'11 Proceedings of the 10th international conference on Ad-hoc, mobile, and wireless networks
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We consider infrastructure-less highly dynamic networks, where connectivity does not necessarily hold, and the network may actually be disconnected at every time instant. These networks are naturally modeled as time-varying graphs. Clearly the task of designing protocols for these networks is less difficult if the environment allows waiting (i.e., it provides the nodes with store-carry-forward-like mechanisms such as local buffering) than if waiting is not feasible. We provide a quantitative corroboration of this fact in terms of the expressivity of the corresponding time-varying graph; that is in terms of the language generated by the feasible journeys in the graph. We prove that the set of languages Lnowait when no waiting is allowed contains all computable languages. On the other end, we prove that Lwait is just the family of regular languages. This gap is a measure of the computational power of waiting. We also study bounded waiting; that is when waiting is allowed at a node only for at most d time units. We prove the negative result that L wait[d] = Lnowait.