Implementing set objects in dynamic distributed systems

This paper considers a set object, i.e., a shared object allowing users (processes) to add and remove elements to the set, as well as taking consistent snapshots of its content. Specifically, we show that there not exists any protocol implementing a set object, using finite memory, when the underlying distributed system is eventually synchronous and affected by continuous arrivals and departures of processes (phenomenon also known as churn). Then, we analyze the relationship between system model assumptions and object specification in order to design protocols implementing the set object using finite memory. Along one direction (strengthening the system model), we propose a protocol implementing the set object in synchronous distributed systems and, along the other direction (weakening the object specification), we introduce the notion of a k-bounded set object proposing a protocol working on an eventually synchronous system.