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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

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Abstract. Collaborative editors consist of a group of users editing a shared document. The Operational Transformation (OT) approach is used for supporting optimistic replication in these editors. It allows the users to concurrently update the shared data and exchange their updates in any order since the convergence of all replicas, i.e. the fact that all users view the same data, is ensured in all cases. However, designing algorithms for achieving convergence with the OT approach is a critical and challenging issue. In this paper, we address the verification of OT algorithms with a model-checking technique. We formally define, using tool UPPAAL, the behavior and the convergence requirement of the collaborative editors, as well as the abstract behavior of the environment where these systems are supposed to operate. So, we show how to exploit some features of such systems and the tool UPPAAL to attenuate the severe state explosion problem. We have been able to show that if the number of users exceeds 2 then the convergence property is not satisfied for five OT algorithms. A counterexample is provided for every algorithm.

Reconciliating divergent data is an important issue in concurrent engineering, mobile computing and software configuration management. Currently, a lot of synchronizers or merge tools perform reconciliations. However, they do not define what is the correctness of their synchronisation. In this paper, we propose to use a transformational approach as the basic model for reasonning about synchronisation. We propose an algorithm and specific transformation functions that realize a file system synchronisation. Unlike classic synchronizers, our synchronizer ensures properties of convergence, causality and intention preservation and is extensible to new data types.