Deciding Reachability in Mobile Ambients with Name Restriction

We investigate the reachability problem for fragments of the Mobile Ambients, a powerful model for distributed and mobile computation. By using a connection with associative-commutative term rewriting, we prove that reachability is decidable in the open-free fragment of pure Mobile Ambients with name restriction and weak reduction semantics. Processes in this model have three sources of infiniteness: depth of ambients, width of parallel composition, and number of restricted names. Our work extends similar results obtained for public fragments of Mobile Ambients.