Interplay between (Im)perfectness, Synchrony and Connectivity: The Case of Reliable Message Transmission
For unconditionally reliable message transmission (URMT) in synchronous directed networks of n nodes, a subset of which may be malicious, it is well-known that the minimum connectivity requirements for zero-error (perfect) protocols to exist is strictly higher than those where a negligible yet non-zero error probability is allowed (Monte Carlo protocols) . In this work, we study the minimum connectivity requirements for the existence of (a) synchronous Las Vegas, (b) asynchronous Monte Carlo, and (c) asynchronous Las Vegas protocols for URMT.
Interestingly, we prove that in any network, a synchronous Las Vegas URMT protocol exists if and only if an asynchronous Monte Carlo URMT protocol exists too. We further show that in any network, an asynchronous Las Vegas URMT protocol exists if and only if a synchronous perfect protocol exists as well. Thus, our results establish an interesting interplay between (im)perfectness, synchrony and connectivity for the case of URMT.
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