The Life in 1-Consensus

TL;DR

This paper introduces a new deterministic shared memory object, $ ext{WRN}_{k}$, that surpasses read-write registers in strength but cannot implement 2-processor consensus, challenging existing conjectures about consensus number 1 objects.

Contribution

It presents the $ ext{WRN}_{k}$ object, demonstrating that objects with consensus number 1 can be strictly stronger than read-write registers, refuting prior conjectures.

Findings

$ ext{WRN}_{k}$ is stronger than read-write registers for $k extgreater 2$.

$ ext{WRN}_{k}$ cannot implement 2-processor consensus.

Refutes the conjecture that all consensus number 1 objects are equivalent to read-write registers.

Abstract

This paper introduces the atomic Write and Read Next ($\text{WRN}_{k}$) deterministic shared memory object, that for any $k\ge3$, is stronger than read-write registers, but is unable to implement $2$-processor consensus. In particular, it refutes the conjecture claiming that every deterministic object of consensus number $1$ is computationally equivalent to read-write registers.