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On reliable message diffusion

We study the diffusion problem in asynchronous systems with transient communication failures, presented by Skeen, Finkelstein and Cristian. We show that two levels of knowledge are necessary in each run of a protocol solving the problem. Two levels are sufficient, as long as communication in the system is not required to subside. Finally, we show that any subsiding protocol solving the problem must either deliver ack-ack messages and hence attain three levels of knowledge in every run, or use three different types of messages.