Completeness theorem for a class of synchronization objects

We study a class of synchronization objects in shared memory concurrent systems, which we call common2. This class contains read-modify-write objects that commute (e.g. fetch-and-add), or overwrite (e.g. swap) and queue shared objects. It is known that this class is contained in the consensus number 2 class of objects [Her91a], and most of the commonly used objects with consensus number 2 are included in it. We show that any object in the common2 class can implement any other object in the class, in a system with an arbitrary number of processes. In fact we show that the objects in common2 are implementable from any object with consensus number 2. The common2 class is in particular interesting since the strongest objects most contemporary processors support are in this class, e.g. either test-and-set or swap while concurrent operating systems constructs installed on any machine may usually rely on any other primitive in this class. Additional implications of our result are: (1) The existence of fault-tolerant self implementations of objects in common2, (2) improvements in the efficiency of randomized constructions of several objects in common2 from read/write registers, and (3) low contention constructions of objects in common2.