Reactive Turing machines extend classical Turing machines with a facility to model observable interactive behaviour. We call a behaviour (finitely) executable if, and only if, it is equivalent to the behaviour of a (finite) reactive Turing machine. In this paper, we study the relationship between executable behaviour and behaviour that can be specified in the $\pi$-calculus. We establish that every finitely executable behaviour can be specified in the $\pi$-calculus up to divergence-preserving branching bisimilarity. The converse, however, is not true due to (intended) limitations of the model of reactive Turing machines. That is, the $\pi$-calculus allows the specification of behaviour that is not finitely executable up to divergence-preserving branching bisimilarity. We shall prove, however, that if the finiteness requirement on reactive Turing machines and the associated notion of executability is relaxed to orbit-finiteness, then the $\pi$-calculus is executable up to (divergence-insensitive) branching bisimilarity.

中文翻译：

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$\pi$-微积分是行为完备且轨道有限可执行的

反应式图灵机扩展了经典的图灵机，具有对可观察的交互行为进行建模的功能。当且仅当它等价于（有限）反应式图灵机的行为时，我们才称其为（有限）可执行的。在本文中，我们研究了可执行行为与可以在 $\pi$-演算中指定的行为之间的关系。我们确定每个有限可执行行为都可以在 $\pi$-演算中指定，直到保持分歧的分支双相似性。然而，由于反应式图灵机模型的（预期）限制，相反的情况并非如此。也就是说，$\pi$-calculus 允许对不有限可执行的行为进行规范，直到保持发散性的分支双相似性。然而，我们将证明，