带负权重的一时钟定价时间博弈
One-Clock Priced Timed Games with Negative Weights
AI总结：
本文研究带负权重的一时钟定价时间博弈，针对简单子类提出伪多项式时间算法计算最优值及策略，并推广至负重置无环类，但完整类可判定性仍开放。
摘要：
定价时间博弈是在定价时间自动机上进行的双人零和博弈（其位置和转移分别用权重标记，模拟在状态中花费时间和执行动作的成本）。玩家的目标分别是最小化和最大化到达目标位置的成本。我们考虑具有一个时钟和任意整数权重的定价时间博弈，并证明对于其中重要的子类（所谓的简单定价时间博弈），可以在伪多项式时间内计算玩家能够达到的最优值及其相关的最优策略。作为附带结果，我们还证明了一时钟定价时间博弈是确定的，并且我们可以利用关于简单定价时间博弈的结果来解决更一般的所谓负重置无环定价时间博弈类（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完整定价时间博弈类的可判定性状态仍然开放。
英文摘要：
Priced timed games are two-player zero-sum games played on priced timed automata (whose locations and transitions are labeled by weights modelling the cost of spending time in a state and executing an action, respectively). The goals of the players are to minimise and maximise the cost 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 them (the so-called simple priced timed games), one can compute, in pseudo-polynomial 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.
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