Jupiter Made Abstract, and Then Refined

Collaborative text editing systems allow multiple users to concurrently edit the same document, which can be modeled by a replicated list object. In the literature, there is a family of operational transformation (OT)-based Jupiter protocols for replicated lists, including AJupiter, XJupiter, and CJupiter. They are hard to understand due to the subtle OT technique, and little work has been done on formal verification of complete Jupiter protocols. Worse still, they use quite different data structures. It is unclear about how they are related to each other, and it would be laborious to verify each Jupiter protocol separately. In this work, we make contributions towards a better understanding of Jupiter protocols and the relation among them. We first identify the key OT issue in Jupiter and present a generic solution. We summarize several techniques for carrying out the solution, including the data structures to maintain OT results and to guide OTs. Then, we propose an implementation-independent AbsJupiter protocol. Finally, we establish the (data) refinement relation among these Jupiter protocols (AbsJupiter included). We also formally specify and verify the family of Jupiter protocols and the refinement relation among them using TLA⁺ (TLA stands for “Temporal Logic of Actions”) and the TLC model checker. To our knowledge, this is the first work to formally specify and verify a family of OT-based Jupiter protocols and the refinement relation among them. It would be helpful to promote a rigorous study of OT-based protocols.