Space-Optimal Majority in Population Protocols

Population protocols are a popular model of distributed computing, in which n agents with limited local state interact randomly, and cooperate to collectively compute global predicates. Inspired by recent developments in DNA programming, an extensive series of papers, across different communities, has examined the computability and complexity characteristics of this model. Majority, or consensus, is a central task in this model, in which agents need to collectively reach a decision as to which one of two states A or B had a higher initial count. Two metrics are important: the time that a protocol requires to stabilize to an output decision, and the state space size that each agent requires to do so. It is known that majority requires Ω(log logn) states per agent to allow for fast (poly-logarithmic time) stabilization, and that O(log n) states are sufficient. Thus, there is an exponential gap between the space upper and lower bounds for this problem. This paper addresses this