Many applications model their data in a general-purpose storage format such as JSON. This data structure is modified by the application as a result of user input. Such modifications are well understood if performed sequentially on a single copy of the data, but if the data is replicated and modified concurrently on multiple devices, it is unclear what the semantics should be. In this paper we present an algorithm and formal semantics for a JSON data structure that automatically resolves concurrent modifications such that no updates are lost, and such that all replicas converge towards the same state (a conflict-free replicated datatype or CRDT). It supports arbitrarily nested list and map types, which can be modified by insertion, deletion and assignment. The algorithm performs all merging client-side and does not depend on ordering guarantees from the network, making it suitable for deployment on mobile devices with poor network connectivity, in peer-to-peer networks, and in messaging systems with end-to-end encryption.

International audienceCollaborative 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 precise specification of their desired behavior, and several of these protocols have been shown not to satisfy even basic expectations. This paper provides a precise specification of a replicated list object, which models the core func-tionality 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, and we show that one of these protocols almost matches the bound

Geographically distributed systems often rely on replicated eventually consistent data stores to achieve availability and performance. To resolve conflicting updates at different replicas, researchers and practitioners have proposed specialized consistency protocols, called replicated data types, that implement objects such as registers, counters, sets or lists. Reasoning about replicated data types has however not been on par with comparable work on abstract data types and concurrent data types, lacking specifications, correctness proofs, and optimality results.To fill in this gap, we propose a framework for specifying replicated data types using relations over events and verifying their implementations using replication-aware simulations. We apply it to 7 existing implementations of 4 data types with nontrivial conflictresolution strategies and optimizations (last-writer-wins register, counter, multi-value register and observed-remove set). We also present a novel technique for obtaining lower bounds on the worstcase space overhead of data type implementations and use it to prove optimality of 4 implementations. Finally, we show how to specify consistency of replicated stores with multiple objects axiomatically, in analogy to prior work on weak memory models. Overall, our work provides foundational reasoning tools to support research on replicated eventually consistent stores.