Expressiveness modulo bisimilarity of regular expressions with parallel composition

The languages accepted by finite automata are precisely the l anguages denoted by regular expressions. In contrast, finite automata may exhibit behaviours t hat cannot be described by regular expressions up to bisimilarity. In this paper, we consider extensi ons 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 expre ssions 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 expressiv eness. Finally, we prove that the theory of regular expressions with ACP-style parallel composition and encapsulation is expressive enough to express all finite automata modulo bisimilarity. Our resu lts extend the expressiveness results obtained by Bergstra, Bethke and Ponse for process algebras with (the binary variant of) Kleene’s star operation.