A framework for proving the self-organization of dynamic systems

TL;DR

This paper provides a rigorous formalization of self-organization in dynamic systems, characterizing different classes through properties related to system entropy, and analyzing their limits via case studies.

Contribution

It introduces a formal framework for defining and analyzing self-organization, including classes based on liveness and safety, and applies it to real-world protocols and systems.

Findings

Different classes of self-organization characterized by entropy-related properties

Analysis of limits and capabilities of existing self-organized protocols

Framework supports designing more robust dynamic system algorithms

Abstract

This paper aims at providing a rigorous definition of self- organization, one of the most desired properties for dynamic systems (e.g., peer-to-peer systems, sensor networks, cooperative robotics, or ad-hoc networks). We characterize different classes of self-organization through liveness and safety properties that both capture information re- garding the system entropy. We illustrate these classes through study cases. The first ones are two representative P2P overlays (CAN and Pas- try) and the others are specific implementations of \Omega (the leader oracle) and one-shot query abstractions for dynamic settings. Our study aims at understanding the limits and respective power of existing self-organized protocols and lays the basis of designing robust algorithm for dynamic systems.