A Behavioural Theory for a π-calculus with Preorders

We study the behavioural theory of piP, a pi-calculus featuring restriction as the only binder. In contrast with calculi such as Fusions and Chi, reduction in piP generates a preorder on names rather than an equivalence relation. We present two characterisations of barbed congruence in piP: the fi rst is based on a compositional LTS, and the second is an axiomatisation. The results in this paper bring out basic properties of piP, mostly related to the interplay between the restriction operator and the preorder on names