Concurrent Undo Operations in Collaborative Environments Using Operational Transformation.

In distributed collaborative systems, replicated objects, shared by users, are subject to concurrency constraints. All methods [4, 13, 18, 15, 16, 19, 22] proposed to serialize concurrent operations and achieve copies convergence of replicated objects are based on the use of Operational Transformations. In this context, giving the user the ability to undo an operation has been recognized as a difficult problem [1, 2, 3, 12, 14, 20, 21]. The few general propositions to solve the problem sometimes compromise copies convergence and/or users' intention, insofar as the Operational Transformations used are unsuitable for undo. This paper has a twofold objective. Firstly, it aims to highlight two general conditions (named C3 and C4) that need to be satisfied by any transformation adapted to undo. Secondly, it presents a general undo algorithm based on the definition of a generic undo-fitted transformation, which automatically verifies these conditions. The interest of the proposed method is that the undoing of an operation obeys to the same processing as the one used for regular operations in collaborative systems such as [15,19].