Topological Self-Stabilization with Name-Passing Process Calculi

Topological self-stabilization is the ability of a distributed system to have its nodes themselves establish a meaningful overlay network. Independent from the initial network topology, it converges to the desired topology via forwarding, inserting, and deleting links to neighboring nodes. We adapt a linearization algorithm, originally designed for a shared memory model, to asynchronous message-passing. We use an extended localized π-calculus to model the algorithm and to formally prove its essential self-stabilization properties: closure and weak convergence for every arbitrary initial configuration, and strong convergence for restricted cases. 1998 ACM Subject Classification F.2.2 Nonnumerical Algorithms and Problems, F.3.1 Specifying and Verifying and Reasoning about Programs