操作变换方法的一致性研究
On Consistency of Operational Transformation Approach
AI总结：
本文通过控制器合成技术证明，对于仅包含插入和删除操作的基本签名，操作变换函数无法同时满足保证收敛所需的TP1和TP2两个性质。
摘要：
操作变换（OT）方法用于许多协同编辑器中，允许一组用户并发更新共享对象的副本，并以任意顺序交换它们的更新。该方法的基本思想是在对对象副本执行任何接收到的更新操作之前对其进行变换。这种变换旨在确保对象的不同副本收敛，即使操作以不同的顺序执行。然而，设计实现收敛的变换函数是一个关键且具有挑战性的问题。事实上，文献中提出的变换函数都被证明是不正确的。在本文中，我们研究了由插入和删除操作改变的共享字符串的变换函数的存在性。从理论角度来看，两个性质——称为TP1和TP2——是确保收敛的充分必要条件。使用控制器合成技术，我们表明存在一些变换函数仅满足插入和删除操作基本签名的TP1。事实上，使用这些简单签名不可能同时满足TP1和TP2两个性质。
英文摘要：
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.
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