The inclusion problem is one of the common problems in real-time systems. The general form of this problem is undecidable; however, the time-bounded verification of inclusion problem is decidable for timed automata. In this study, we propose a new discretization technique to verify the inclusion problem. The proposed technique is applied to a non-Zeno timed automaton with an upper bound that does not contain a non-reachable space for each transition. The new approach is based on the generation of timed bounded discretized language that represents an abstraction of timed words in the form of a set of a countable number of discrete timed words. A discrete timed word aggregates all timed words that share the same actions and their execution times that create the time continuous intervals. The lower and the upper bounds of an interval in a discrete timed word is defined by the minimum and maximum execution times associated to a given transition-run. In addition, we propose the verification schema of the inclusion between two timed bounded discretized languages generated by two non-Zeno timed automata.

中文翻译：

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基于时间有界离散语言的包含时间有界验证

包含问题是实时系统中的常见问题之一。这个问题的一般形式是不确定的；然而，包含问题的时间限制验证对于时间自动机是可判定的。在这项研究中，我们提出了一种新的离散化技术来验证包含问题。所提出的技术应用于一个非 Zeno 定时自动机，其上限不包含每个转换的不可到达空间。新方法基于定时有界离散语言的生成，该语言以一组可计数的离散定时词的形式表示定时词的抽象。离散的定时词聚合了所有共享相同动作的定时词及其执行时间，从而创建了时间连续间隔。离散定时字中间隔的下限和上限由与给定转换运行相关联的最小和最大执行时间定义。此外，我们提出了由两个非 Zeno 定时自动机生成的两个定时有界离散语言之间包含的验证模式。