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We present for the first time a complete solution to the problem of provingthe correctness of a concurrency control algorithm for collaborative texteditors against the standard consistency model. The success of our approachstems from the use of comprehensive stringwise operational transformations,which appear to have escaped a formal treatment until now. Because thesetransformations sometimes lead to an increase in the number of operations asthey are transformed, we cannot use inductive methods and adopt the novel ideaof decreasing diagrams instead. We also base our algorithm on a client-servermodel rather than a peer-to-peer one, which leads to the correct application ofoperational transformations to both newly generated and pending operations. Andlastly we solve the problem of latency, so that our algorithm works perfectlyin practice. The result of these innovations is the first ever formally correctconcurrency control algorithm for collaborative text editors together with afast, fault tolerant and highly scalable implementation.

Operational Concurrency Control in the Face of Arbitrary Scale and Latency