2015
Expressiveness modulo bisimilarity of regular expressions with parallel composition
Publication
Publication
Mathematical Structures in Computer Science , Volume Firstview
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 modulo bisimilarity. Then, we prove that
replacing the operation for pure interleaving by ACP-style parallel composition gives a
further increase in expressiveness, still insufficient, however, to facilitate the expression of all
finite automata up to bisimilarity. 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.
Additional Metadata | |
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Cambridge U.P. | |
Mathematical Structures in Computer Science | |
Organisation | Directie |
Baeten, J., Luttik, B., Muller, T., & van Tilburg, P. (2015). Expressiveness modulo bisimilarity of regular expressions with parallel composition. Mathematical Structures in Computer Science, Firstview. |