Expressiveness modulo Bisimilarity of Regular Expressions with Parallel Composition (Extended Abstract)

Jos C. M. Baeten
(Eindhoven University of Technology, The Netherlands)
Bas Luttik
(Eindhoven University of Technology, The Netherlands)
Tim Muller
(University of Luxembourg, Luxembourg)
Paul van Tilburg
(Eindhoven University of Technology, The Netherlands)

The languages accepted by finite automata are precisely the languages denoted by regular expressions. In contrast, finite automata may exhibit behaviours that cannot be described by regular expressions up to bisimilarity. In this paper, we consider extensions of the theory of regular expressions with various forms of parallel composition and study the effect on expressiveness. First we prove that adding pure interleaving to the theory of regular expressions strictly increases its expressiveness up to bisimilarity. Then, we prove that replacing the operation for pure interleaving by ACP-style parallel composition gives a further increase in expressiveness. Finally, we prove that the theory of regular expressions with ACP-style parallel composition and encapsulation is expressive enough to express all finite automata up to bisimilarity. Our results extend the expressiveness results obtained by Bergstra, Bethke and Ponse for process algebras with (the binary variant of) Kleene's star operation.

In Sibylle Fröschle and Frank D. Valencia: Proceedings 17th International Workshop on Expressiveness in Concurrency (EXPRESS'10), Paris, France, August 30th, 2010, Electronic Proceedings in Theoretical Computer Science 41, pp. 1–15.
Published: 28th November 2010.

ArXived at: http://dx.doi.org/10.4204/EPTCS.41.1 bibtex PDF

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