Analyzing Linearizability in Relativistic Distributed Systems

2026-06-29

AI Summary

This work addresses the breakdown of traditional linearizability in distributed systems under relativistic effects, where events cannot be totally ordered by absolute time. Building upon the relativistic linearizability framework introduced by Gilbert and Golab, we establish, for the first time, correctness guarantees for classical asynchronous algorithms—specifically, replicated state machines and variants of the ABD register—that strictly surpass those implied by Jayanti’s theorem. By integrating relativistic consistency theory, formal verification techniques, and shared object modeling, we rigorously prove that these algorithms satisfy relativistic linearizability, thereby providing the long-missing formal correctness proofs for their behavior in relativistic settings.

Abstract

Einstein's theory of relativity correctly predicted that time is relative, and subject to both kinematic and gravitational dilation. Therefore, executions of distributed systems cannot always be modeled as sequences of events totally ordered according to wall clock time. To address this fundamental problem, Gilbert and Golab formulated a generalization of Herlihy and Wing's linearizability property for shared objects, which they called \emph{relativistic linearizability}, and introduced a collection of theoretical tools to facilitate rigorous analysis. While they conjectured that several widely-studied classically linearizable algorithms are also relativistically linearizable, their work stopped short of presenting formal proofs of correctness, as pointed out recently by Jayanti. In this paper, we explain how Gilbert and Golab's techniques can be used to establish relativistic linearizability for a replicated state machine, as well as variations of the widely studied read/write register construction of Attiya, Bar-Noy and Dolev (ABD). Our results establish a stronger form of relativistic linearizability than Jayanti's central theorem for these asynchronous algorithms.

Problem

• relativistic linearizability
• distributed systems
• linearizability
• relativity
• shared objects

Innovation

• relativistic linearizability
• distributed systems
• replicated state machine
• ABD register
• formal verification