Milner (1984) introduced a process semantics for regular expressions as process graphs. Unlike for the language semantics, where every regular (that is, DFA-accepted) language is the interpretation of some regular expression, there are finite process graphs that are not bisimilar to the process interpretation of any regular expression. For reasoning about graphs that are expressible by regular expressions modulo bisimilarity it is desirable to have structural representations of process graphs in the image of the interpretation. For '1-free' regular expressions, their process interpretations satisfy the structural property LEE (loop existence and elimination). But this is not in general the case for all regular expressions, as we show by examples. Yet as a remedy, we describe the possibility to recover the property LEE for a close variant of the process interpretation. For this purpose we refine the process semantics of regular expressions to yield process graphs with 1-transitions, similar to silent moves for finite-state automata.

中文翻译：

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正则表达式的过程语义的结构受限过程图

Milner（1984）引入了正则表达式作为过程图的过程语义。与语言语义不同，在语言语义中，每种正则（即DFA接受的）语言都是对某些正则表达式的解释，而有限的过程图与任何正则表达式的过程解释都不一样。为了对可由正则表达式模双相似性表示的图进行推理，希望在解释图像中具有过程图的结构表示。对于“无1”正则表达式，其过程解释满足结构属性LEE（循环存在和消除）。但这并非所有正则表达式都适用，正如我们通过示例所示。作为一种补救措施 我们描述了在过程解释的近似变体中恢复特性LEE的可能性。为此，我们改进了正则表达式的过程语义，以产生具有1个过渡的过程图，类似于有限状态自动机的无声移动。