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An Equational Relation for Ambient Calculus

Ambient calculus is a process algebra designed by Cardelli and Gordon of Microsoft Research for describing mobile agents. Many approaches for expressing concurrent computation have been developed and some of them treat higher order processes.

In the higher order framework, processes, the subjects of the computation, can be sent by other processes and keep computing in other locations. This framework can express the situation such that a process moves around on a network environment and keeps collecting information (mobile Web searching agent) or a process enters into a field and the field itself is also a process (hierarchal mobile agent). Ambient calculus can model various kinds of those mobile computations by the hierarchy of ambients.

An ambient consists of a pair of brackets which has a name and contains its action. For example, `$a[\mbox{\it in $b$}]$' is an ambient where `$a$' is the name and `in $b$' is the action of the ambient. An ambient can contain ambients too, thus, a process of ambient calculus is composed by the composition and the hierarchy of ambients.

Contextual Equivalence is an equivalence relation proposed by Gordon ambient calculus Intuitively, two processes $A$ and $B$ are contextually equivalent, if for any process with a hole ${\cal C}()$ (we call this process a context), we can observe the same sets of the names in the computations of ${\cal C}(A)$ and ${\cal C}(B)$.

We found there are contextually equivalent processes which have different properties when we defined the external choice operation using only parallel composition and restriction primitives.

Thus, we introduce another equivalence relation to distinguish those processes.
 

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