The Las-Vegas processor identity problem (how and when to be unique)

One of the fundamental problems in distributed computing is how identical processes with identical local memory can choose unique IDs provided they can flip a coin. The variant considered is the asynchronous shared memory model (atomic registers), and the basic correctness requirement is that upon termination the processes must always have unique IDs. The authors study this problem from several viewpoints. On the positive side, they present the first Las-Vegas protocol that solves the problem. The protocol terminates in (optimal) O(log n) expected time, using O(n) shared memory space, where n is the number of participating processes. On the negative side, they show that there is no Las-Vegas protocol unless n is known precisely, and that no finite-state Las-Vegas protocol can work under schedules that may depend on the history of the shared variable. For the case of arbitrary adversary, they present a Las-Vegas protocol that uses O(n) unbounded registers.<>