This article studies a large class of two-player perfect-information turn-based parity games on infinite graphs, namely, those generated by collapsible pushdown automata. The main motivation for studying these games comes from the connections from collapsible pushdown automata and higher-order recursion schemes, both models being equi-expressive for generating infinite trees. Our main result is to establish the decidability of such games and to provide an effective representation of the winning region as well as of a winning strategy. Thus, the results obtained here provide all necessary tools for an in-depth study of logical properties of trees generated by collapsible pushdown automata/recursion schemes.

中文翻译：

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可折叠下推奇偶校验游戏

本文研究了无限图上的一大类两人完美信息回合制奇偶博弈，即由可折叠下推自动机生成的博弈。研究这些游戏的主要动机来自可折叠下推自动机和高阶递归方案的联系，这两种模型对于生成无限树都是等价的。我们的主要结果是建立此类游戏的可判定性，并提供获胜区域和获胜策略的有效表示。因此，这里获得的结果为深入研究由可折叠下推自动机/递归方案生成的树的逻辑属性提供了所有必要的工具。