Priced timed games are two-player zero-sum games played on priced timed automata (whose locations and transitions are labeled by weights modelling the price of spending time in a state and executing an action, respectively). The goals of the players are to minimise and maximise the price to reach a target location, respectively. We consider priced timed games with one clock and arbitrary integer weights and show that, for an important subclass of theirs (the so-called simple priced timed games), one can compute, in exponential time, the optimal values that the players can achieve, with their associated optimal strategies. As side results, we also show that one-clock priced timed games are determined and that we can use our result on simple priced timed games to solve the more general class of so-called negative-reset-acyclic priced timed games (with arbitrary integer weights and one clock). The decidability status of the full class of priced timed games with one-clock and arbitrary integer weights still remains open.

中文翻译：

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具有任意权重的一时钟价计时游戏

定价定时游戏是在定价定时自动机上玩的两人零和游戏（其位置和转换由权重标记，分别对在状态中花费时间和执行动作的价格进行建模）。玩家的目标是分别最小化和最大化到达目标位置的价格。我们考虑具有一个时钟和任意整数权重的定价计时游戏，并表明，对于它们的一个重要子类（所谓的简单定价计时游戏），可以在指数时间内计算玩家可以获得的最佳值，及其相关的最优策略。作为副结果，我们还表明，单时钟定价的计时游戏是确定的，并且我们可以在简单定价的计时游戏上使用我们的结果来解决更一般的一类所谓的负重置非循环定价的计时游戏（具有任意整数权重和一个时钟）。具有一个时钟和任意整数权重的全类定价计时游戏的可判定性状态仍然开放。