On Consistency of Operational Transformation Approach

TL;DR

This paper investigates the theoretical conditions for convergence in Operational Transformation (OT) systems, demonstrating that certain properties are necessary but cannot be simultaneously satisfied with basic insert and delete operations.

Contribution

It provides a formal analysis of the properties required for OT convergence and shows the impossibility of satisfying all conditions with simple operation signatures.

Findings

TP1 property can be satisfied with basic insert/delete operations

TP2 property cannot be satisfied simultaneously with TP1 for simple signatures

Some transformation functions meet only TP1, highlighting limitations in OT design

Abstract

The Operational Transformation (OT) approach, used in many collaborative editors, allows a group of users to concurrently update replicas of a shared object and exchange their updates in any order. The basic idea of this approach is to transform any received update operation before its execution on a replica of the object. This transformation aims to ensure the convergence of the different replicas of the object, even though the operations are executed in different orders. However, designing transformation functions for achieving convergence is a critical and challenging issue. Indeed, the transformation functions proposed in the literature are all revealed incorrect. In this paper, we investigate the existence of transformation functions for a shared string altered by insert and delete operations. From the theoretical point of view, two properties - named TP1 and TP2 - are necessary and sufficient to ensure convergence. Using controller synthesis technique, we show that there are some transformation functions which satisfy only TP1 for the basic signatures of insert and delete operations. As a matter of fact, it is impossible to meet both properties TP1 and TP2 with these simple signatures.