Consensus power makes (some) sense!

This paper presents partial results of an ongoing investigation into the computability power of processors that are computing wait-free while synchronizing through various deterministic linearizable synchronization objects. Our main result is that any task over ≤ In processors, solvable using objects that cannot implement n + 1 process consensus, can be solved using only n process consensus objects. We also identify two new object implementation notions: protocol-implementation and taskimplementation. We show that objects that cannot implement n + 1 process consensus are protocolimplementable by n process consensus objects. A corollary of the latter result is that the class of objects that do not implement n+1 process consensus is closed under composition (i.e., in the terminology of [17], Herlihy's hierarchy is robust). With these two results, we substantiate for the first time Herlihy's consensus number n notion for objects with fan-in greater than n.