We study the realizability problem for concurrent recursive programs: given a distributed system architecture and a sequential specification over words, find a distributed automata implementation that is equivalent to the specification. This problem is well-studied as far as finite-state processes are concerned, and it has a solution in terms of Zielonka’s Theorem. We lift Zielonka’s Theorem to the case where processes are recursive and modeled as visibly pushdown (or, equivalently, nested-word) automata. However, contrarily to the finite-state case, it is undecidable whether a specification is realizable or not. Therefore, we also consider suitable underapproximation techniques from the literature developed for multi-pushdown systems, and we show that they lead to a realizability framework with effective algorithms.

中文翻译：

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并发递归程序的可实现性

我们研究并发递归程序的可实现性问题：给定一个分布式系统架构和一个顺序规范，找到一个等价于规范的分布式自动机实现。就有限状态过程而言，这个问题得到了很好的研究，并且根据 Zielonka 定理有一个解决方案。我们将 Zielonka 定理提升到过程是递归的并且建模为可见下推（或等效地，嵌套词）自动机的情况。然而，与有限状态情况相反，规范是否可实现是不可判定的。因此，我们还从为多下推系统开发的文献中考虑了合适的欠逼近技术，并且我们表明它们导致了具有有效算法的可实现性框架。