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

Clemens Grabmayer
(Gran Sasso Science Institute, L'Aquila)

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.

In Patrick Bahr: Proceedings 11th International Workshop on Computing with Terms and Graphs (TERMGRAPH 2020), Online, 5th July 2020, Electronic Proceedings in Theoretical Computer Science 334, pp. 29–45.
Published: 8th February 2021.

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