An ordered approach to solving parity games in quasi-polynomial time and quasi-linear space
An ordered approach to solving parity games in quasi-polynomial time and quasi-linear space
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DOI：
10.1007/s10009-019-00509-3
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发表时间：
2019-06-01
影响因子：
1.5
通讯作者：
Wojtczak, Dominik
中科院分区：
文献类型：
--
作者：
Fearnley, John;Jain, Sanjay;Wojtczak, Dominik
平价游戏在模型检查和合成中起着重要作用。在他们的论文中，Calude等人。最近表明，这些游戏可以在准多项式时间内解决。我们证明它们的算法可以有效地实现：我们将其数据结构用作进度度量，从而可以做出向后实现，而不是对游戏的完整解开。为了实现这一目标，必须对其技术进行许多更改，其中主要的方法是为对抗玩家增加力量，以确定她的理性运动而不改变游戏结果。我们为准多项式算法提供了第一个实施，在少数示例中对其进行了测试，并提供了许多侧面结果，包括次要算法改进，状态数量和边缘的Quasi-Bi线性复杂性和固定数量的边缘Calude等人的算法的颜色，与我们的方法相关的复杂性指数匹配，我们将其与最近提出的寄存器指数进行比较。
Parity games play an important role in model checking and synthesis. In their paper, Calude et al. have recently shown that these games can be solved in quasi-polynomial time. We show that their algorithm can be implemented efficiently: we use their data structure as a progress measure, allowing for a backward implementation instead of a complete unravelling of the game. To achieve this, a number of changes have to be made to their techniques, where the main one is to add power to the antagonistic player that allows for determining her rational move without changing the outcome of the game. We provide a first implementation for a quasi-polynomial algorithm, test it on small examples, and provide a number of side results, including minor algorithmic improvements, a quasi-bi-linear complexity in the number of states and edges for a fixed number of colours, matching lower bounds for the algorithm of Calude et al., and a complexity index associated to our approach, which we compare to the recently proposed register index.