We show that the minimization of visibly pushdown automata is NP-complete. This result is obtained by introducing immersions, that recognize multiple languages (over a usual, non-visible alphabet) using a common deterministic transition graph, such that each language is associated with an initial state and a set of final states. We show that minimizing immersions is NP-complete, and reduce this problem to the minimization of visibly pushdown automata.

中文翻译：

---

可见下推自动机的最小化是 NP 完全的

我们表明，可见下推自动机的最小化是 NP 完全的。这个结果是通过引入沉浸式获得的，沉浸式使用通用的确定性转换图识别多种语言（在通常的、不可见的字母表上），这样每种语言都与一个初始状态和一组最终状态相关联。我们表明最小化沉浸是 NP 完全的，并将这个问题减少到最小化可见下推自动机。