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

Structure-Constrained Process Graphs for the Process Semantics of Regular Expressions