Specification and Implementation of Replicated List: The Jupiter Protocol Revisited

TL;DR

This paper revisits the Jupiter protocol for replicated lists, introducing CJupiter with a new data structure to prove it satisfies the weak list specification, confirming the protocol's correctness in collaborative systems.

Contribution

The paper introduces CJupiter, a novel data structure, and proves its equivalence to Jupiter, demonstrating it satisfies the weak list specification for replicated lists.

Findings

CJupiter is equivalent to Jupiter.

CJupiter satisfies the weak list specification.

The new data structure simplifies reasoning about replica states.

Abstract

The replicated list object is frequently used to model the core functionality of replicated collaborative text editing systems. Since 1989, the convergence property has been a common specification of a replicated list object. Recently, Attiya et al. proposed the strong/weak list specification and conjectured that the well-known Jupiter protocol satisfies the weak list specification. The major obstacle to proving this conjecture is the mismatch between the global property on all replica states prescribed by the specification and the local view each replica maintains in Jupiter using data structures like 1D buffer or 2D state space. To address this issue, we propose CJupiter (Compact Jupiter) based on a novel data structure called $n$-ary ordered state space for a replicated client/server system with $n$ clients. At a high level, CJupiter maintains only a single $n$-ary ordered state space which encompasses exactly all states of each replica. We prove that CJupiter and Jupiter are equivalent and that CJupiter satisfies the weak list specification, thus solving the conjecture above.