Algebraic File Synchronization: Adequacy and Completeness

TL;DR

This paper develops an algebraic framework for file synchronization, introducing new commands and proofs to ensure accurate detection and reconciliation of diverging data replicas in distributed systems.

Contribution

It presents a novel, symmetric set of filesystem commands and rigorous proofs that improve the algebraic modeling of synchronization processes, ensuring correctness and completeness.

Findings

Algorithms for update detection and reconciliation are proven correct.

New algebraic commands increase information content and reduce edge cases.

The framework provides a theoretical basis for error-free synchronization applications.

Abstract

With distributed computing and mobile applications, synchronizing diverging replicas of data structures is a more and more common problem. We use algebraic methods to reason about filesystem operations, and introduce a simplified definition of conflicting updates to filesystems. We also define algorithms for update detection and reconciliation and present rigorous proofs that they not only work as intended, but also cannot be improved on. To achieve this, we introduce a novel, symmetric set of filesystem commands with higher information content, which removes edge cases and increases the predictive powers of our algebraic model. We also present a number of generally useful classes and properties of sequences of commands. While these results are often intuitive, providing exact proofs for them is far from trivial. They contribute to our understanding of this special type of algebraic model, and toward building more complete algebras of filesystem trees and extending algebraic approaches to other data storage protocols. They also form a theoretical basis for specifying and guaranteeing the error-free operation of applications that implement an algebraic approach to synchronization.