The computational power of concurrent data types has been the focus of
much recent research. Herlihy showed that such power may be measured
by the type's ability to implement wait-free consensus. Jayanti argued
that this ability could be measured in different ways, depending, for
example, on whether or not read/write registers could be used in an i
mplementation. He demonstrated the significance of this distinction by
exhibiting a nondeterministic type whose ability to implement consens
us was increased with the availability of registers. We show that regi
sters cannot increase the ability to implement wait-free consensus of
any deterministic type or of any type that can, without them, implemen
t consensus for at least two processes. These results significantly im
pact the study of the wait-free hierarchies of concurrent data types.
In particular, the combination of these results with other recent work
suggests that Jayanti's h(m) hierarchy is robust for certain classes
of deterministic types.