# Wait-Free Universality of Consensus in the Infinite Arrival Model

## TL;DR

This paper proves that consensus remains a universal object in an infinite arrival model of distributed systems and introduces a universal construction with a weak log, expanding the understanding of consensus in dynamic environments.

## Contribution

It extends the universality of consensus to the infinite arrival model and proposes a new universal construction with implementations using consensus and compare&swap.

## Key findings

- Consensus is universal even with infinitely many processes.
- A weak log construction is proposed for the infinite arrival model.
- Two implementations of the weak log are provided, using consensus and compare&swap.

## Abstract

In classical asynchronous distributed systems composed of a fixed number n of processes where some proportion may fail by crashing, many objects do not have a wait-free linearizable implementation (e.g. stacks, queues, etc.). It has been proved that consensus is universal in such systems, which means that this system augmented with consensus objects allows to implement any object that has a sequential specification. To this end, many universal constructions have been proposed in systems augmented with consensus objects or with different equivalent objects or special hardware instructions (compare&swap, fetch&add, etc.). In this paper, we consider a more general system model called infinite arrival model where infinitely many processes may arrive and leave or crash during a run. We prove that consensus is still universal in this more general model. For that, we propose a universal construction. As a first step we build a weak log for which we propose two implementations using consensus objects for the first and the compare&swap special instruction for the other.