Given the versatility of timed automata a huge body of work has evolved that considers extensions of timed automata. One extension that has received a lot of interest is timed automata with a, possibly unbounded, stack, also called the pushdown timed automata (PDTA) model. While different algorithms have been given for reachability in different variants of this model, most of these results are purely theoretical and do not give rise to efficient implementations. One main reason for this is that none of these algorithms (and the implementations that exist) use the so-called zone-based abstraction, but rely either on the region-abstraction or other approaches, which are significantly harder to implement. In this paper, we show that a naive extension using simulations of the zone based reachability algorithm for the control state reachability problem of timed automata is not sound in the presence of a stack. To understand this better we give an inductive rule based view of the zone reachability algorithm for timed automata. This alternate view allows us to analyze and adapt the rules to also work for pushdown timed automata. We obtain the first zone-based algorithm for PDTA which is terminating, sound and complete. We implement our algorithm in the tool TChecker and perform experiments to show its efficacy, thus leading the way for more practical approaches to the verification of pushdown timed systems.

中文翻译：

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基于区域的快速下推定时自动机可达性算法

鉴于定时自动机的多功能性，大量的工作已经发展到考虑到定时自动机的扩展。一个广受关注的扩展是带有可能无界堆栈的定时自动机，也称为下推定时自动机 (PDTA) 模型。虽然针对该模型的不同变体的可达性给出了不同的算法，但这些结果中的大部分都是纯理论的，并不能产生有效的实现。一个主要原因是这些算法（以及现有的实现）都没有使用所谓的基于区域的抽象，而是依赖于区域抽象或其他方法，这些方法很难实现。在本文中，我们表明，使用基于区域的可达性算法的模拟来解决定时自动机的控制状态可达性问题的朴素扩展在存在堆栈的情况下是不合理的。为了更好地理解这一点，我们给出了定时自动机区域可达性算法的基于归纳规则的视图。这种替代视图使我们能够分析和调整规则，使其也适用于下推定时自动机。我们获得了第一个基于区域的 PDTA 算法，它是终止的、健全的和完整的。我们在工具 TChecker 中实施我们的算法并进行实验以证明其有效性，从而为验证下推定时系统的更实用方法开辟了道路。为了更好地理解这一点，我们给出了定时自动机区域可达性算法的基于归纳规则的视图。这种替代视图使我们能够分析和调整规则，使其也适用于下推定时自动机。我们获得了第一个基于区域的 PDTA 算法，它是终止的、健全的和完整的。我们在工具 TChecker 中实施我们的算法并进行实验以证明其有效性，从而为验证下推定时系统的更实用方法开辟了道路。为了更好地理解这一点，我们给出了定时自动机区域可达性算法的基于归纳规则的视图。这种替代视图使我们能够分析和调整规则，使其也适用于下推定时自动机。我们获得了第一个基于区域的 PDTA 算法，它是终止的、健全的和完整的。我们在工具 TChecker 中实施我们的算法并进行实验以证明其有效性，从而为验证下推定时系统的更实用方法开辟了道路。