Expressive Power of Broadcast Consensus Protocols

Population protocols are a formal model of computation by identical, anonymous mobile agents interacting in pairs. Their computational power is rather limited: Angluin et al. have shown that they can only compute the predicates over N^k expressible in Presburger arithmetic. For this reason, several extensions of the model have been proposed, including the addition of devices called cover-time services, absence detectors, and clocks. All these extensions increase the expressive power to the class of predicates over N^k lying in the complexity class NL when the input is given in unary. However, these devices are difficult to implement, since they require that an agent atomically receives messages from all other agents in a population of unknown size; moreover, the agent must know that they have all been received. Inspired by the work of the verification community on Emerson and Namjoshi\u27s broadcast protocols, we show that NL-power is also achieved by extending population protocols with reliable broadcasts, a simpler, standard communication primitive

Probabilistic Population Protocol Models

Population protocols are a relatively novel computational model in which very resource-limited anonymous agents interact in pairs with the goal of computing predicates. We consider the probabilistic version of this model, which naturally allows to consider the setup in which a small probability of an incorrect output is tolerated. The main focus of this thesis is the question of confident leader election, which is an extension of the regular leader election problem with an extra requirement for the eventual leader to detect its uniqueness. Having a confident leader allows the population protocols to determine the convergence of its computations. This behaviour of the model is highly beneficial and was shown to be feasible when the original model is extended in various ways. We show that it takes a linear in terms of the population size number of interactions for a probabilistic population protocol to have a non-zero fraction of agents in all reachable states, starting from a configuration with all agents in the same state. This leads us to a conclusion that confident leader election is out of reach even with the probabilistic version of the model