Weighted Timed Games (WTG for short) are the most widely used model to describe controller synthesis problems involving real-time issues. Unfortunately, they are notoriously difficult, and undecidable in general. As a consequence, one-clock WTGs have attracted a lot of attention, especially because they are known to be decidable when only non-negative weights are allowed. However, when arbitrary weights are considered, despite several recent works, their decidability status was still unknown. In this paper, we solve this problem positively and show that the value function can be computed in exponential time (if weights are encoded in unary).

翻译：加权时间游戏（简称WTG）是描述涉及实时问题的控制器综合问题最广泛使用的模型。不幸的是，它们通常非常困难，且普遍不可判定。因此，单时钟WTG引起了广泛关注，尤其是在仅允许非负权重时它们已知是可判定的。然而，尽管最近有几项研究，但当考虑任意权重时，其可判定性状态仍然未知。在本文中，我们积极解决了这一问题，并表明值函数可以在指数时间内计算（如果权重以一元编码表示）。