An automata-based approach for synchronizable mailbox communication

TL;DR

This paper presents an automata-based method to analyze the compliance of mailbox communication systems with round-based policies, proving the problem is Pspace-complete without round size restrictions.

Contribution

It introduces a novel automata-based approach to determine the Pspace-completeness of mailbox communication system compliance with round-based policies.

Findings

The problem is Pspace-complete for mailbox systems with no round size limit.

The automata-based approach precisely characterizes the complexity of related questions.

The method extends previous work by removing fixed round size constraints.

Abstract

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.