Parametrised Constants and Replication for Spatial Mobility

Parametrised replication and replication are common ways of expressing infinite computation in process calculi. While parametrised constants can be encoded using replication in the

π

-calculus, this changes in the presence of spatial mobility as found in e.g. the distributed

π

-calculus and the calculus of mobile ambients. Here, processes are located at sites and can migrate between them.

In this paper we say that an encoding is local if it does not introduce extra migration. We first study this property for the distributed

π

-calculus where locations can be dynamically created. If the set of reachable sites is static an encoding exists, but we also show that parametrised constants can not be encoded in the full calculus. The locality requirement supplements widely accepted encoding criteria. It appears to be a natural property in spatial calculi where links and locations can fail.

The versions of the distributed

π

-calculus with parametrised constants and replication are incomparable. On the other hand, we shall see that there exists a simple encoding of recursion in mobile ambients.