The Consensus Hierarchy is not

The consensus hierarchy characterizes the strength of a shared object by its ability to solve the consensus problem in a wait-free manner. A robust hierarchy has the additional property that objects at lower levels cannot be combined in any way to construct objects at higher levels of the hierarchy. Several variations of the consensus hierarchy have appeared in the literature, and it has been shown that if there is a robust hierarchy it is either Jayanti's hierarchy h r m or a coarsening of h r m. This paper shows that if non-deterministic objects are permitted to make choices drawn from the set of natural numbers and protocols are restricted to those with running times bounded by a function of input size, then the consensus hierarchy h r m is not robust. 1. Introduction The notion of consensus number, introduced by Herlihy (1991), provides a framework for comparing the power of diierent models of shared memory wait-free computation. Herlihy deened the consensus number of an object to be the maximum number of deterministic processes that could solve consensus using a single copy of the object together with a collection of atomic registers. Objects that can be used to solve consensus for any number of