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Causality, Influence, and Computation in Possibly Disconnected Dynamic Networks

In this work, we study the propagation of influence and computation in dynamic distributed systems. We focus on broadcasting models under a worst-case dynamicity assumption which have received much attention recently. We drop for the first time in worst-case dynamic networks the common instantaneous connectivity assumption and require a minimal temporal connectivity. Our temporal connectivity constraint only requires that another causal influence occurs within every time-window of some given length. We establish that there are dynamic graphs with always disconnected instances with equivalent temporal connectivity to those with always connected instances. We present a termination criterion and also establish the computational equivalence with instantaneous connectivity networks. We then consider another model of dynamic networks in which each node has an underlying communication neighborhood and the requirement is that each node covers its local neighborhood within any time-window of some given length. We discuss several properties and provide a protocol for counting, that is for determining the number of nodes in the network.