The notion of separating automata was introduced by Bojanczyk and Czerwinski for understanding the first quasipolynomial time algorithm for parity games. In this paper we show that separating automata is a powerful tool for constructing algorithms solving games with combinations of objectives. We construct two new algorithms: the first for disjunctions of parity and mean payoff objectives, matching the best known complexity, and the second for disjunctions of mean payoff objectives, improving on the state of the art. In both cases the algorithms are obtained through the construction of small separating automata, using as black boxes the existing constructions for parity objectives and for mean payoff objectives.

中文翻译：

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使用分离自动机组合目标的新算法

分离自动机的概念是由 Bojanczyk 和 Czerwinski 引入的，用于理解奇偶游戏的第一个拟多项式时间算法。在本文中，我们展示了分离自动机是构建解决具有目标组合的游戏的算法的强大工具。我们构建了两个新算法：第一个用于奇偶校验和平均收益目标的分离，匹配最知名的复杂性，第二个用于平均收益目标的分离，改进了现有技术。在这两种情况下，算法都是通过构建小型分离自动机获得的，将现有的用于奇偶目标和平均收益目标的构造用作黑盒。