Power of multi-objects (extended abstract)

We consider shared memory systems that support multi-object operations in which processes may simultaneously access several objects in one atomic operation. We provide upper and lower bounds on the synchronization power (consensus number) of multi-object systems as a function of the type and the number of objects that may be simultaneously accessed in one atomic operation. These bounds imply that known classifications of component objects fail to characterize the synchronization power of their combination. In particular, we show that in the context of multi-objects, fetch & add objects are less powerful than swap objects, which in turn are less powerful than queue objects. This stands in contrast to the fact that swap can be implemented from fetch & add. Herein we introduce a restricted notion of implementation, called direct implementation. We show that, if an object Y has a direct implementation from X then also the Y based multi-object can be implemented from the X based multi-object. Following the above, we derive results such as: there is no direct implementations of a swap object, and queue object from any collection of commutative objects (e.g., fetch & add, test & set).