An Equivalence Relation for the Typed Ambient Calculus

The ambient calculus is a process algebra designed for describing mobile processes. It has a layered structure of ambients that enables us to describe not only mobile processes but also the world in which the processes move around such as computer networks and freight systems. When we describe such a system with ambients, however, malicious processes can destroy nodes of the network or alter the construction of the system. Thus, several mobility types for the ambient calculus have been proposed to enable us to give each node desirable characteristics that prevent malicious processes from acting harmfully. Gordon and Cardelli, the originators of the ambient calculus, also defined an equivalence relation for the untyped ambient calculus. Our previous work pointed out that there exist identified processes up to the relation that have different properties, and it refined the relation so that we can discriminate those processes. This paper shows that the original relation and our previous relation are no longer available for the typed ambient calculus and it presents another relation that is suitable.