We revisit finite-state communicating systems with round-based communication under mailbox semantics. Mailboxes correspond to one FIFO buffer per process (instead of one buffer per pair of processes in peer-to-peer systems). Round-based communication corresponds to sequences of rounds in which processes can first send messages, then only receive (and receives must be in the same round as their sends). A system is called synchronizable if every execution can be re-scheduled into an equivalent execution that is a sequence of rounds. Previous work mostly considered the setting where rounds have fixed size. Our main contribution shows that the problem whether a mailbox communication system complies with the round-based policy, with no size limitation on rounds, is Pspace-complete. For this we use a novel automata-based approach, that also allows to determine the precise complexity (Pspace) of several questions considered in previous literature.

@article{paperbot3984,
  title = {An automata-based approach for synchronizable mailbox communication},
  author = {Romain Delpy and Anca Muscholl and Grégoire Sutre},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 22, Issue 2},
  year = {2026},
  doi = {10.46298/lmcs-22(2:24)2026}
}