The main result of this paper is that computing the value of a one-clock priced timed game (OCPTG) is PSPACE-hard. Along the way, we provide a family of OCPTGs that have an exponential number of event points. Both results hold even in very restricted classes of games such as DAGs with treewidth three. Finally, we provide a number of positive results, including polynomial-time algorithms for even more restricted classes of OCPTGs such as trees.

中文翻译：

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一个时钟定价的定时游戏是 PSPACE 难的

本文的主要结果是，计算单时钟定价计时游戏 (OCPTG) 的价值是 PSPACE-hard 的。在此过程中，我们提供了一系列具有指数数量事件点的 OCPTG。这两个结果甚至在非常有限的游戏类别中也成立，例如树宽为 3 的 DAG。最后，我们提供了许多积极的结果，包括用于更受限制的 OCPTG 类（例如树）的多项式时间算法。