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.