Population Protocols with Convergence Detection

Abstract

This paper focuses on pairwise interaction-based protocols, and proposes an universal mechanism that allows each agent to locally detect that the system has converged to the sought configuration with high probability. To illustrate our mechanism, we use it to detect the instant at which the proportion problem is solved. Specifically, let nA (resp. nB) be the number of agents that initially started in state $A$ (resp. B) and γA= nA/n, where $n$ is the total number of agents. Our protocol guarantees, with a given precision ε > 0 and any high probability 1 - 6, that after O ($n$ ln($n$ /δ)) interactions, any queried agent that has set the detection flag will output the correct value of the proportion γA of agents which started in state A, by maintaining no more than O (ln(n) / ε) integers. We are not aware of any such results. Simulation results illustrate our theoretical analysis.