On the Computational Power of Shared Objects

We propose a new classification for evaluating the strength of shared objects. The classification is based on finding, for each object of type

o

, the strongest progress condition for which it is possible to solve consensus for

any

number of processes, using any number of objects of type

o

and atomic registers. We use the strongest progress condition to associate with each object a number call the

power number

of that object. Objects with higher power numbers are considered stronger. Then, we define the

power hierarchy

which is an infinite hierarchy of objects such that the objects at level

i

of the hierarchy are exactly those objects with power number

i

. Comparing our classification with the traditional one which is based on fixing the progress condition (namely, wait-freedom) and finding the largest number of processes for which consensus is solvable, reveals interesting results. Our equivalence and extended universality results, provide a deeper understanding of the nature of the relative computational power of shared objects.