Collaborative text editing systems allow users to concurrently edit a shared document, inserting and deleting elements (e.g., characters or lines). There are a number of protocols for collaborative text editing, but so far there has been no abstract, high-level specification of their desired behavior, which is decoupled from their actual implementation. Several of these protocols have been shown not to satisfy even basic expectations. This paper provides a precise specification of a replicated abstract list object, which models the core functionality of replicated systems for collaborative text editing. We define a strong list specification, which we prove is implemented by an existing protocol, as well as a weak list specification, which admits additional protocol behaviors.

A major factor determining the efficiency and practical feasibility of a collaborative text editing protocol is the space overhead of the metadata that the protocol must maintain to ensure correctness. We show that for a large class of list protocols, implementing either the strong or the weak list specification requires a metadata overhead that is at least linear in the number of elements deleted from the list. The class of protocols to which this lower bound applies includes all list protocols that we are aware of, in particular CRDT and OT protocols, and we show that one of these protocols almost matches the bound. The result holds for peer-to-peer protocols, even if the network guarantees causal atomic broadcast. The result also holds for the metadata cost at the clients in client/server protocols.¹

协作文本编辑系统允许用户同时编辑共享文档，插入和删除元素（例如，字符或行）。有许多用于协作文本编辑的协议，但是到目前为止，还没有关于其所需行为的抽象的，高级的规范，这些规范与它们的实际实现是脱节的。已经证明这些协议中的几个甚至不能满足基本期望。本文提供了复制摘要列表对象的精确规范，该对象为协作文本编辑建模了复制系统的核心功能。我们定义了一个强列表规范，我们证明它是由现有协议实现的，而弱列表规范是 列表规范，它接受其他协议行为。

决定协作文本编辑协议的效率和实际可行性的主要因素是协议必须保持以确保正确性的元数据的空间开销。我们表明，对于一大类列表协议，实现强列表或弱列表规范要求的元数据开销至少是线性的从列表中删除的元素数。下限适用的协议类别包括我们知道的所有列表协议，尤其是CRDT和OT协议，并且我们证明这些协议之一几乎与边界匹配。即使网络保证了因果的原子广播，结果也适用于对等协议。结果还适用于客户端/服务器协议中客户端的元数据成本。^1个