On the Expressiveness of Internal Mobility in Name-Passing Calculi

We consider πI, a fragment of the π-calculus where only exchange of private names among processes is permitted (internal mobility). The calculus πI enjoys a simpler mathematical treatment, very close to that of CCS. In particular, πI avoids the concept of substitution. We provide an encoding from the asynchronous π-calculus to πI and then prove that two processes are barbed equivalent in π-calculus if and only if their translations in πI cannot be distinguished, under barbed bisimilarity, by any translated static context. The result shows that, in name-passing calculi, internal mobility is the essential ingredient as far as expressiveness is concerned.