Population protocols with unreliable communication
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Population protocols are a model of distributed computation intended for the study of networks of independent computing agents with dynamic communication structure. Each agent has a finite number of states, and communication opportunities occur nondeterministically, allowing the agents involved to change their states based on each other's states. Multiple variations of that model have been studied. In most of them the situation of temporary impossibility of communication between some agents is natural. On the other hand, the models usually assume atomic interactions, i.e. either all the agents update their state or none do. In practice, ensuring that in case of a communication problem an interaction is recognised as successful either by all participants or by nobody has performance and implementation complexity costs. In the present paper we study unreliable models based on population protocols and their variations from the point of view of expressive power. We model the effects of non-atomic interaction. We show that for a general definition of unreliable protocols with constant-storage agents such protocols can only compute predicates computable by immediate observation population protocols. Immediate observation population protocols are inherently tolerant of unreliable communication and keep their expressive power under a wide range of fairness conditions. We prove it via a structural lemma that can also be applied for other settings requiring guaranteed eventual correctness. We also prove that adding unreliability reduces expressive power non-monotonically, and show that a large class of message-based models becomes strictly less expressive than immediate observation.
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