Weak vs. Self vs. Probabilistic Stabilization

TL;DR

This paper compares different stabilization concepts in distributed systems, showing that weak stabilization is more powerful than self-stabilization and can be transformed into probabilistic self-stabilization under certain conditions.

Contribution

It formally proves the relative strength of weak, self, and probabilistic stabilization, and demonstrates how weak stabilization can be converted into probabilistic self-stabilization in practical scenarios.

Findings

Weak stabilization is strictly stronger than self-stabilization.

Deterministic weak-stabilizing protocols can be transformed into probabilistic self-stabilizing ones.

Weak stabilization offers practical advantages due to easier design and proof processes.

Abstract

Self-stabilization is a strong property that guarantees that a network always resume correct behavior starting from an arbitrary initial state. Weaker guarantees have later been introduced to cope with impossibility results: probabilistic stabilization only gives probabilistic convergence to a correct behavior. Also, weak stabilization only gives the possibility of convergence. In this paper, we investigate the relative power of weak, self, and probabilistic stabilization, with respect to the set of problems that can be solved. We formally prove that in that sense, weak stabilization is strictly stronger that self-stabilization. Also, we refine previous results on weak stabilization to prove that, for practical schedule instances, a deterministic weak-stabilizing protocol can be turned into a probabilistic self-stabilizing one. This latter result hints at more practical use of weak-stabilization, as such algorthms are easier to design and prove than their (probabilistic) self-stabilizing counterparts.