Anomalies in the Wait-Free Hierarchy

Abst rac t . We considel' the hierarchy of wait-free shared objects, and show that this hierarchy does not express the computational power of shared objects. We prove that there are objects that are classified high in the hierarchy, yet, they can not implement objects that are classified much lower in the hierarchy. Our main result is: for any two levels kl > k2 in the hierarchy, there are shared objects X1 and X2 that belong to kl and k2, respectively, such that X1 can not implement X2. (We allow the specifications of the shared objects to be non deterministic.) This result implies not only that the current definition of the wait-free hierarchy does not express the computationa] power of shared objects, but also that there is no other hierarchy that does.