Spatial Congruence for the Ambients Is Decidable Spatial Congruence for the Ambients Is Decidable

The ambient calculus of Cardelli and Gordon is a process calculus for describing mobile computation where processes may reside within a hierarchy of locations, called ambients. The dynamic semantics of this calculus is presented in a chemical style that allows for a compact and simple formulation. In this semantics, an equivalence relation, the spatial congruence, is deened on the top of an unlabelled transition system, the reduction system. Reduction is used to represent a real step of evolution (in time), while spatial congruence is used to identify processes up to particular (spatial) rearrangements. In this paper, we show that it is decidable to check whether two ambient calculus processes are spatially congruent, or not. Our proof is based on a natural and intuitive interpretation of ambient processes as edge-labelled nite-depth trees. This allows us to concentrate on the subtle interaction between two key operators of the ambient calculus, namely restriction , that accounts for the dynamic generation of new location names, and replication, used to encode recursion. The result of our study is the deenition of an algorithm to decide spatial congruence and a deenition of a normal form for processes that is useful in the proof of interesting equivalence laws.