A Possible Solution to the Impossible Membership Problem

Abstract

This paper presents a solvable specification and gives an algorithm for the Group Membership Problem in asynchronous systems with crash failures. Our specification requires processes to maintain a consistent history in their sequence of views. This allows processes to order failures and recoveries in time and simplifies the programming of high level applications. Previous work proved that the Group Membership Problem cannot be solved in asynchronous systems with crash failures. We circumvent this impossibility result building a weaker, yet non-trivial specification. We show that our solution is an improvement upon previous attempts to solve this problem using a weaker specification. We also relate our solution to other methods, and give a classification of progress properties that can be achieved under different models.