Executable Behaviour and the $\pi$-Calculus

Reactive Turing machines extend Turing machines with a facility to model observable interactive behaviour. A behaviour is called executable if, and only if, it is behaviourally equivalent to the behaviour of a reactive Turing machine. In this paper, we study the relationship between executable behaviour and behaviour that can be specified in the π-calculus. We establish that all executable behaviour can be specified in the π-calculus up to divergence-preserving branching bisimilarity. For the converse, however, we need to let go of the requirement of divergence-preservation: we exhibit behaviour specifiable in the π-calculus that is not executable up to divergence-preserving behavioural equivalence, but do obtain that every behaviour definable in the π-calculus is executable up to the version of branching bisimilarity that does not preserve divergence.