# Preserving Stabilization while Practically Bounding State Space

## TL;DR

This paper introduces an algorithm that transforms stabilizing programs with unbounded variables into ones with bounded variables and practical physical time, ensuring stabilization with limited space.

## Contribution

It presents a novel transformation algorithm applicable to various problems, enabling stabilization with bounded variables and physical time, extending prior work on non-stabilizing programs.

## Key findings

- Applicable to logical clocks, vector clocks, mutual exclusion, leader election, and Paxos.
- Enables stabilization with bounded variables in diverse systems.
- Can be combined with existing methods to bound counters in stabilization.

## Abstract

Stabilization is a key dependability property for dealing with unanticipated transient faults, as it guarantees that even in the presence of such faults, the system will recover to states where it satisfies its specification. One of the desirable attributes of stabilization is the use of bounded space for each variable. In this paper, we present an algorithm that transforms a stabilizing program that uses variables with unbounded domain into a stabilizing program that uses bounded variables and (practically bounded) physical time. While non-stabilizing programs (that do not handle transient faults) can deal with unbounded variables by assigning large enough but bounded space, stabilizing programs that need to deal with arbitrary transient faults cannot do the same since a transient fault may corrupt the variable to its maximum value. We show that our transformation algorithm is applicable to several problems including logical clocks, vector clocks, mutual exclusion, leader election, diffusing computations, Paxos based consensus, and so on. Moreover, our approach can also be used to bound counters used in an earlier work by Katz and Perry for adding stabilization to a non-stabilizing program. By combining our algorithm with that earlier work by Katz and Perry, it would be possible to provide stabilization for a rich class of problems, by assigning large enough but bounded space for variables.