Abstract. This paper compares the expressiveness of ambient calculi against different dialects of the pi-calculus. Cardelli and Gordon encoded the asynchronous pi-calculus into their calculus of Mobile Ambients (MA). Zimmer has shown that the synchronous pi-calculus without choice can be encoded in pure (no communication) Safe Ambients. We show that pure MA without restriction has symmetric electoral systems, that is, it is possible to solve the problem of electing a leader in a symmetric network. By the work of Palamidessi, this implies that pure MA without restriction is not encodable (under certain conditions) in the picalculus with separate choice. We adapt the work of Carbone and Maffeis to show that pure MA cannot be encoded (under certain other conditions) into the pi-calculus with mixed choice (but without matching). 1

Recently, various process calculi have been introduced which are suited for the modelling of mobile computation and in particular the mobility of program code; a prominent example is the ambient calculus. Due to the complexity of the involved spatial reduction, there is — in contrast to the situation in standard process algebra — up to now no satisfying coalgebraic representation of a mobile process calculus. Here, we discuss a coalgebraic denotational semantics for the ambient calculus, viewed as a step towards a generic coalgebraic framework for modelling mobile systems. Crucial features of our modelling are a set of GSOS style transition rules for the ambient calculus, a hardwiring of the so-called hardening relation in the functorial signature, and a set-based treatment of hidden name sharing. The formal representation of this framework is cast in the algebraic-coalgebraic specification language CoCasl.

This paper compares the expressiveness of different fragments of ambient calculi via