Interpreting a finitary pi-calculus in differential interaction nets

We propose and study a translation of a pi-calculus without sums nor recursion into an untyped version of differential interaction nets. We define a transition system of labeled processes and a transition system of labeled differential interaction nets. We prove that our translation from processes to nets is a bisimulation between these two transition systems. This shows that differential interaction nets are sufficiently expressive for representing concurrency and mobility, as formalized by the pi-calculus.Our study will concern essentially a replication-free fragment of the pi-calculus, but we shall also give indications on how to deal with a restricted form of replication.