We consider the problem of simulating traditional population protocols underweaker models of communication, which include one-way interactions (as opposedto two-way interactions) and omission faults (i.e., failure by an agent to readits partner's state during an interaction), which in turn may be detectable orundetectable. We focus on the impact of a leader, and we give a completecharacterization of the models in which the presence of a unique leader in thesystem allows the construction of simulators: when simulations are possible, wegive explicit protocols; when they are not, we give proofs of impossibility.Specifically, if each agent has only a finite amount of memory, the simulationis possible only if there are no omission faults. If agents have an unboundedamount of memory, the simulation is possible as long as omissions aredetectable. If an upper bound on the number of omissions involving the leaderis known, the simulation is always possible, except in the one-way model inwhich one side is unable to detect the interaction.
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