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 (both for mailbox and peer-to-peer automata): 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 for mailbox automata.

中文翻译：

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关于系统的k-同步性

在本文中，我们研究 k 同步性的概念：如果系统的任何执行，直到重新排序因果独立的动作，可以分为一系列 k 有界交互阶段，则系统是 k 同步的。我们展示了两个结果（邮箱和点对点自动机）：首先，可达性问题对于 k 同步系统是可判定的；其次，成员问题（给定的系统是否是 k 同步的）也是可判定的。我们的证明解决了之前尝试证明邮箱自动机的这两个结果的几个重要问题。