On the Computational Power of Simple Dynamics

This work presents a set of analytical results regarding some elementary randomized protocols, called \emph{dynamics}, for solving some fundamental computational problems. New techniques for analyzing the processes that arise from such dynamics are presented, together with concrete examples on how to build efficient and robust distributed algorithms for some important tasks using these processes as a black-box. More specifically, we analyze several dynamics such as the 3-Majority, the Averaging and the Undecided-State ones, and we show how to use them to solve fundamental problems such as plurality consensus, community detection (including the reconstruction problem in the stochastic block model), and bit dissemination (rumor spreading). We focus mainly on unstructured and random interaction models, and we also deal with scenarios in which the communication is affected by noise or when a self-stabilizing protocol is required.