All of Us Are Smarter than Any of Us: Nondeterministic Wait-Free Hierarchies Are Not Robust

A wait-free hierarchy Herlihy91, Jayanti93] classiies object types on the basis of their strength in supporting wait-free implementations of other types. Such a hierarchy is robust if it is impossible to implement objects of types that it classiies as \strong" by combining objects of types that it classiies as \weak". We prove that, if nondeterministic types are allowed, the only wait-free hierarchy that is robust is the trivial one, which lumps all types into a single level. In particular, the Consensus hierarchy (the most closely studied wait-free hierarchy) is not robust. Our result implies that, in general, it is not possible to determine the power of a concurrent system that supports a given set of primitive object types by reasoning about the power of each primitive type in isolation.