Ideal Stabilization

TL;DR

This paper introduces the concept of ideal stabilization, where every system state is legitimate, enabling precise recovery specifications and analyzing conditions for ideal stabilization in various distributed algorithms.

Contribution

It formally defines ideal stabilization, establishes necessary conditions, and demonstrates its application by proving several well-known protocols are ideally stabilizing.

Findings

No ideally stabilizing solution for leader election.

Proved ideal stabilization for conflict manager, alternator, feedback propagation, and alternating bit protocol.

Abstract

We define and explore the concept of ideal stabilization. The program is ideally stabilizing if its every state is legitimate. Ideal stabilization allows the specification designer to prescribe with arbitrary degree of precision not only the fault-free program behavior but also its recovery operation. Specifications may or may not mention all possible states. We identify approaches to designing ideal stabilization to both kinds of specifications. For the first kind, we state the necessary condition for an ideally stabilizing solution. On the basis of this condition we prove that there is no ideally stabilizing solution to the leader election problem. We illustrate the utility of the concept by providing examples of well-known programs and proving them ideally stabilizing. Specifically, we prove ideal stabilization of the conflict manager, the alternator, the propagation of information with feedback and the alternating bit protocol.