On the k-synchronizability for mailbox systems

Asynchronous bounded or unbounded message passing is ubiquitous in communication-centric systems. When modelling distributed scenarios, it is important to understand whether buffers are bounded or not. In this paper, we work on the notion of k-synchronizability: a system is k-synchronizable if any of its executions, up to reordering causally independent actions, can be divided into a succession of k-bounded interaction phases. We show two results: first, the reachability problem is decidable for k-synchronizable systems; second, the membership problem (whether a given system is k-synchronizable) is decidable as well. Our proofs fix several important issues in previous attempts to prove these two results.