  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.
