Deciding reachability problems in Turing-complete fragments of Mobile Ambients

Abstract

The calculus of Mobile Ambients was proposed by Cardelli and Gordon as a foundational calculus for mobile computing. Since its introduction, the computational strength and the decidability of properties have been investigated for several fragments and variants of the standard calculus. We consider the problem of reachability and characterise a public (that is, restriction-free) fragment for which it is decidable. This fragment is obtained by removing the open capability and restricting the application of the replication operator to guarded processes only. This decidability result may appear surprising in combination with the fact that the same fragment was shown to be Turing complete by Maffeis and Phillips. Finally, we extend our decidability result in two ways: we first prove the decidability of a more general property called target reachability (according to which the target of interest for the reachability analysis consists of a possibly infinite set of processes) and then show that our decidability results also hold for a more general calculus, which includes the sophisticated communication mechanisms of Boxed Ambients, which is the most relevant variant of Mobile Ambients without the open capability.