On the viability of the deterministic consensus hierarchy

Abstract

A recent paper by Afek, Ellen, and Gafni introduced a family of deterministic objects Om,k, for m,k≥2, with consensus numbers m such that, for each k≥2, Om,k is computationally less powerful than Om,k+1 in systems with at least mk+m+k processes. This paper gives a wait-free implementation of Om,k from (m+1)-consensus objects and registers in systems with finitely many processes. In order to do so, it introduces a new family of objects which helps us to understand the power of m-consensus in a system with more than m processes.