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Operational Transformation is an approach which allows to build real-time groupware tools. This approach requires correct transformation functions. Proving the correction of these transformation functions is very complex and error prone. In this paper, we show how a theorem prover can address this serious bottleneck. To validate our approach, we verified the correctness of state-of-art transformation functions defined on Strings with surprising results. Counter-examples provided by the theorem prover helped us to define new correct transformation functions for Strings.

http://ieeexplore.ieee.org/In collaborative editing, consistency maintenance of the copies of shared data is a critical issue. In the last decade, Operational Transformation (OT) approach revealed as a suitable mechanism for maintaining consistency. Unfortunately, none of the published propositions relying on this approach are able to satisfy the mandatory correctness properties TP1 and TP2 defined in the Ressel's framework. This paper addresses this correctness issue by proposing a new way to model shared state by retaining tombstones when elements are removed. An instantiation of the proposed model for a linear data structure and the related transformation functions are provide

International audienceReal-time Collaborative Editors (RCE) are a class of distributed systems based on the interaction of several users trying to edit simultaneously shared documents, such as articles, wiki pages and programming source code. Operational Transformation (OT) is considered as the efficient and safe method for consistency maintenance in the literature of collaborative editors. Indeed, it is aimed at ensuring copies convergence even though the users's updates are executed in any order on different copies. Unfortunately, existing OT algorithms often fail to achieve this objective. Moreover, these algorithms have limited scalability with the number of users as they use vector timestamps to enforce causality dependency. In this paper, we present a novel coordination model for managing collaborative editing work in a scalable and decentralized fashion. It may be deployed easily on P2P networks as it supports dynamic groups where users can leave and join at any time