The weakest oracle for symmetric consensus in population protocols

Abstract

We consider the symmetric consensus problem, a version of consensus adapted to population protocols, a model for large scale networks of resource-limited mobile sensors. After proving that consensus is impossible in the considered model, we look for oracles to circumvent this impossibility. An oracle is an external (to the system) module providing some information allowing to solve the problem. We define a class of oracles adapted to population protocols, and we prove that an oracle in this class, namely DejaV u, allows to obtain a solution. Finally, and this is the major contribution of the paper, we prove that DejaV u is the weakest oracle for solving the problem.