一句话：引入 good-for-games ω-下推自动机，证明其比确定性 ω-PDA 表达力更强，且相应无限博弈求解为 EXPTIME 完全。
本文引入 good-for-games ω-下推自动机（ω-GFG-PDA），其中非确定性可仅根据已读输入消解，从而使自动机可像确定性自动机一样与博弈、树和其他自动机组合。作者证明 ω-GFG-PDA 比确定性 ω-下推自动机表达力更强，并证明以 ω-GFG-PDA 为获胜条件的无限博弈求解是 EXPTIME 完全的，由此得到一类新的可判定 ω-上下文无关获胜条件及 EXPTIME 的 universality 复杂度。文中还研究该类语言的封闭性质、ω-下推自动机与语言的 good-for-gameness 可判定性，与 ω-可见下推自动机比较，分析消解非确定性所需资源，并证明 ω-GFG-PDA 的 parity index 层级是无穷的。
We introduce good-for-games $\omega$-pushdown automata ($\omega$-GFG-PDA). These are automata whose nondeterminism can be resolved based on the input processed so far. Good-for-gameness enables automata to be composed with games, trees, and other automata, applications which otherwise require deterministic automata. Our main results are 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. Thus, we have identified a new class of $\omega$-contextfree winning conditions for which solving games is decidable. It follows that the universality problem for $\omega$-GFG-PDA 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. Finally, we compare $\omega$-GFG-PDA to $\omega$-visibly PDA, study the resources necessary to resolve the nondeterminism in $\omega$-GFG-PDA, and prove that the parity index hierarchy for $\omega$-GFG-PDA is infinite. This is a corrected version of the paper arXiv:2001.04392v6 published originally on January 7, 2022.