Birrell's Distributed Reference Listing Revisited

The Java RMI collector is arguably the most widely used distributed garbage collector. Its distributed reference listing algorithm was introduced by Birrell in the context of Network Objects, where the description was informal and heavily biased toward implementation. In this paper, we formalise this algorithm in an implementation-independent manner, which allows us to clarify weaknesses of the initial presentation. In particular, we discover cases critical to the correctness of the algorithm that are not accounted for by Birrell. We use our formalisation to derive an invariant-based proof of correctness of the algorithm that avoids notoriously difficult temporal reasoning. Furthermore, we offer a novel graphical representation of the state transition diagram, which we use to provide intuitive explanations of the algorithm and to investigate its tolerance to faults in a systematic manner. Finally, we examine how the algorithm may be optimised, either by placing constraints on message channels or by tightening the coupling between application program and distributed garbage collector.