Parametric timed automata (PTA) are a powerful formalism to model and reason about concurrent systems with some unknown timing delays. In this paper, we address the (untimed) language- and trace-preservation problems: given a reference parameter valuation, does there exist another parameter valuation with the same untimed language, or with the same set of traces? We show that these problems are undecidable both for general PTA and for the restricted class of L/U-PTA, even for integer-valued parameters, or over bounded time. On the other hand, we exhibit decidable subclasses: 1-clock PTA, and 1-parameter deterministic L-PTA and U-PTA. We also consider robust versions of these problems, where we additionally require that the language be preserved for all valuations between the reference valuation and the new valuation.

中文翻译：

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参数定时自动机中的语言保存问题

参数定时自动机 (PTA) 是一种强大的形式主义，可以对具有一些未知时间延迟的并发系统进行建模和推理。在本文中，我们解决了（未计时的）语言和痕迹保存问题：给定参考参数估值，是否存在具有相同非计时语言或相同痕迹集的另一个参数估值？我们表明，这些问题对于一般 PTA 和 L/U-PTA 的受限类都是不可判定的，即使对于整数值参数或有界时间也是如此。另一方面，我们展示了可判定的子类：1 时钟 PTA，以及 1 参数确定性 L-PTA 和 U-PTA。我们还考虑了这些问题的稳健版本，其中我们还要求为参考估值和新估值之间的所有估值保留语言。