We introduce good-for-games $\omega$-pushdown automata ($\omega$-GFG-PDA). These are automata whose nondeterminism can be resolved based on the run constructed thus far. Good-for-gameness enables automata to be composed with games, trees, and other automata, applications which otherwise require deterministic automata. Our main results show that $\omega$-GFG-PDA are more expressive than deterministic $\omega$-pushdown automata and that solving infinite games with winning conditions specified by $\omega$-GFG-PDA is EXPTIME-complete, i.e., we have identified a new class of $\omega$-contextfree winning conditions for which solving games is decidable. This means in particular that the universality problem is in EXPTIME as well. Moreover, we study closure properties of the class of languages recognized by $\omega$-GFG-PDA and decidability of good-for-gameness of $\omega$-pushdown automata and languages.

中文翻译：

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适合游戏的 $\omega$-Pushdown Automata

我们引入了适合游戏的 $\omega$-pushdown 自动机（$\omega$-GFG-PDA）。这些是自动机，其不确定性可以根据迄今为止构建的运行来解决。Good-for-gameness 使自动机能够由游戏、树和其他自动机组成，这些应用程序否则需要确定性自动机。我们的主要结果表明 $\omega$-GFG-PDA 比确定性 $\omega$-pushdown 自动机更具表现力，并且解决具有 $\omega$-GFG-PDA 指定的获胜条件的无限游戏是 EXPTIME-complete，即，我们已经确定了一类新的 $\omega$-contextfree 获胜条件，解决游戏是可判定的。这特别意味着普遍性问题也在 EXPTIME 中。而且，