Snap-Stabilizing Tasks in Anonymous Networks

TL;DR

This paper characterizes which distributed tasks can be solved by snap-stabilizing algorithms in anonymous networks, demonstrating their relation to self-stabilizing tasks and providing a snap-stabilizing version of Mazurkiewicz's enumeration algorithm.

Contribution

It provides a characterization of tasks solvable by snap-stabilizing algorithms in anonymous networks and introduces a snap-stabilizing version of Mazurkiewicz's enumeration algorithm.

Findings

Characterization of snap-stabilizing tasks in anonymous networks

Connection between self-stabilizing and snap-stabilizing tasks

A snap-stabilizing version of Mazurkiewicz's enumeration algorithm

Abstract

We consider snap-stabilizing algorithms in anonymous networks. Self-stabilizing algorithms are well known fault tolerant algorithms : a self-stabilizing algorithm will eventually recover from arbitrary transient faults. On the other hand, an algorithm is snap-stabilizing if it can withstand arbitrary initial values and immediately satisfy its safety requirement. It is a subset of self-stabilizing algorithms. Distributed tasks that are solvable with self-stabilizing algorithms in anonymous networks have already been characterized by Boldi and Vigna in [BV02b]. In this paper, we show how the more demanding snap-stabilizing algorithms can be handled with standard tools for (not stabilizing) algorithms in anonymous networks. We give a characterization of which tasks are solvable by snap-stabilizing algorithms in anonymous networks. We also present a snap-stabilizing version of Mazurkiewicz' enumeration algorithm. This work exposes, from a task-equivalence point of view, the complete correspondence in anonymous networks between self or snap-stabilizing tasks and distributed tasks with various termination detection requirements.