Can an operation both update the state and return a meaningful value in the asynchronous PRAM model?

On an atomic Read-Modify-Write (RMW) object one can read the complete old contents s of the object and simultaneously update its contents as a function δ(s) of the old contents in a single, indivisible, atomic operation. It is known that these RMW objects do not have a wait-free implementation in the asynchronous PRAM model—in which processors can only communicate with each other through atomic read-write registers. For the general case, in which operations P over an object can return a function φP (s) of the old contents s while simultaneously updating the object’s state to δP (s), few results are known. We give several characterisations, in terms of φP (·) and δP (·), of such objects for which no wait-free implementation in the asynchronous PRAM model exists. The resulting objects are remarkably similar to RMW objects. Indeed, we also exhibit two objects satisfying weaker conditions which do have a such a wait-free implementation. Our results suggest that only objects as strong as RMW objects do not have wait-free implementation in the asynchronous PRAM model.