The \(\pi \)-calculus is a well-established theoretical framework for describing mobile and parallel computation using name passing, and a central notion here is that of name binding. Unfortunately, non-trivial properties of \(\pi \)-calculus processes such as termination and bisimilarity are undecidable as a consequence of the fact that the calculus is Turing-powerful. The classes of depth-bounded and name-bounded processes are classes of \(\pi \)-calculus processes that impose constraints on how name binding is used in a process. A consequence of this is that some of the important decision problems that are undecidable for the full calculus now become decidable. However, membership of these classes of processes is undecidable, so it is difficult to make use of the positive decidability results in practice. In this paper we use binary session types to devise two type systems that give a sound and decidable characterization of each of these two properties. If a process is well-typed in our first system, it is depth-bounded. If a process is well-typed in our second, more restrictive type system, it will also be name-bounded.

中文翻译：

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使用会话类型来推理 $$\pi $$ π 演算中的有界性

\(\pi \) 演算是一个完善的理论框架，用于描述使用名称传递的移动和并行计算，这里的核心概念是名称绑定。不幸的是，\(\pi\)-微积分过程的非平凡性质，例如终止和双相似性，是不可判定的，因为微积分是图灵强大的。深度有界和名称有界进程的类是 \(\pi \)-演算进程的类，它们对如何在进程中使用名称绑定施加约束。这样做的结果是，一些对于全微积分来说不可判定的重要决策问题现在变得可判定了。然而，这些类别的过程的成员资格是不可判定的，因此在实践中很难利用积极的可判定性结果。在本文中，我们使用二进制会话类型来设计两种类型系统，这些系统对这两个属性中的每一个都给出了合理且可确定的特征。如果一个进程在我们的第一个系统中是类型良好的，那么它就是深度有界的。如果一个进程在我们的第二个更严格的类型系统中类型良好，它也将是名称有界的。