Common2 extended to stacks and unbounded concurrency

Abstract

Common2, the family of objects that implement and are wait-free implementable from 2 consensus objects, is extended inhere in two ways: First, the stack object is added to the family --- an object that was conjectured not to be in the family. Second, Common2 is investigated in the unbounded concurrency model, whereas until now it was considered only in an n-process model.We show that fetch-and-add, test-and-set, and stack are in Common2 even with respect to this stronger notion of wait-free implementation. This necessitated the wait-free implementation of immediate snapshots in the unbounded concurrency model, which was previously not known to be possible.In addition to extending Common2, the introduction of unbounded-concurrency may help in resolving the Common2 membership problem: If, as conjectured, queue is not implementable for a-priori known concurrency n, then it is definitely not implementable for unbounded concurrency. Proving the latter should be easier than proving the former. In addition we conjecture that the swap object, that has an n-process implementation, does not have an unbounded concurrency implementation.