Pomset automata are an operational model of weak bi-Kleene algebra, which describes programs that can fork an execution into parallel threads, upon completion of which execution can join to resume as a single thread. We characterize a fragment of pomset automata that admits a decision procedure for language equivalence. Furthermore, we prove that this fragment corresponds precisely to series-rational expressions, i.e., rational expressions with an additional operator for bounded parallelism. As a consequence, we obtain a new proof that equivalence of series-rational expressions is decidable.

中文翻译：

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弱双克林代数的等价检验

Pomset 自动机是弱双克林代数的一种操作模型，它描述了可以将执行分叉到并行线程中的程序，完成后可以加入并作为单个线程继续执行。我们描述了一个 pomset 自动机的片段，该片段允许语言等价的决策过程。此外，我们证明这个片段精确地对应于级数有理表达式，即带有用于有界并行的附加运算符的有理表达式。因此，我们获得了一个新的证明，即级数有理表达式的等价性是可判定的。