Analysis of Critical Phenomenon on Gossip Protocol using Back-Ultradiscretization

Critical probability of a cellular automaton is investigated via a novel approach of back-ultradiscretization. Specifically, back-ultradiscretization of a gossip protocol provides a conservative yet analytical lower bound, which is usually hard to be evaluated in the form of cellular automata. Comparison of theoretical and numerical values are provided for several representative grids to evaluate efficacy of the proposed approach.