Boolean programs with multiple recursive threads can be captured as pushdown automata with multiple stacks. This model is Turing complete, and hence, one is often interested in analyzing a restricted class that still captures useful behaviors. In this paper, we propose a new class of bounded under approximations for multi-pushdown systems, which subsumes most existing classes. We develop an efficient algorithm for solving the under-approximate reachability problem, which is based on efficient fix-point computations. We implement it in our tool BHIM and illustrate its applicability by generating a set of relevant benchmarks and examining its performance. As an additional takeaway, BHIM solves the binary reachability problem in pushdown automata. To show the versatility of our approach, we then extend our algorithm to the timed setting and provide the first implementation that can handle timed multi-pushdown automata with closed guards.

中文翻译：

---

重新审视多下推系统的欠近似可达性

具有多个递归线程的布尔程序可以被捕获为具有多个堆栈的下推自动机。该模型是图灵完备的，因此，人们通常对分析仍然捕获有用行为的受限类感兴趣。在本文中，我们为多下推系统提出了一种新的有界下近似类，它包含了大多数现有类。我们开发了一种有效的算法来解决欠近似可达性问题，该算法基于有效的定点计算。我们在我们的工具 BHIM 中实现了它，并通过生成一组相关基准并检查其性能来说明其适用性。作为额外的收获，BHIM 解决了下推自动机中的二元可达性问题。为了展示我们方法的多功能性，