一句话：提出寄存器博弈，为 parity game 给出新的准多项式时间算法，并改进交替奇偶自动机翻译与层级结果。
本文研究 parity game（奇偶博弈）的复杂度这一长期开放问题，提出一种基于“寄存器博弈”的独立新方法。寄存器博弈是奇偶博弈的参数化变体，通过分析其结构，作者得到 parity game 的准多项式时间算法，并为受限类给出多项式算法；同时提出“寄存器指数”这一复杂度度量，以综合刻画优先级分配与底层博弈图的复杂度。论文还利用寄存器博弈把交替 parity 自动机翻译为交替 weak 自动机，仅带来准多项式级大小增长，优于此前的指数级翻译。最后，作者用该框架研究 parity 指数层级：在字上交替 parity 自动机的层级塌缩到 weak 层，在树上严格，而在树与字之间的结构上呈对数级塌缩，即大小为 n 的 parity 树自动机在这类结构上等价于优先级数关于 n 对数的自动机。
The complexity of parity games is a long standing open problem that saw a major breakthrough in 2017 when two quasi-polynomial algorithms were published. This article presents a third, independent approach to solving parity games in quasi-polynomial time, based on the notion of register game, a parameterised variant of a parity game. The analysis of register games leads to a quasi-polynomial algorithm for parity games, a polynomial algorithm for restricted classes of parity games and a novel measure of complexity, the register index, which aims to capture the combined complexity of the priority assignement and the underlying game graph. We further present a translation of alternating parity word automata into alternating weak automata with only a quasi-polynomial increase in size, based on register games; this improves on the previous exponential translation. We also use register games to investigate the parity index hierarchy: while for words the index hierarchy of alternating parity automata collapses to the weak level, and for trees it is strict, for structures between trees and words, it collapses logarithmically, in the sense that any parity tree automaton of size n is equivalent, on these particular classes of structures, to an automaton with a number of priorities logarithmic in n.