一句话：刻画 Σ_0^2 中具有位置策略且含中性字母的目标，并证明平均收益的位置性及完备性结果。
本文研究在任意博弈图上无限时长博弈中，主角是否存在位置策略（无记忆策略）的问题。作者证明：Σ_0^2 中前缀无关、具有位置策略且承认（强）中性字母的目标，恰好可由可数序数上的历史确定单调 co-Büchi 自动机识别。该结果推广了 Kopczyński（ICALP 2006）提出的判定准则，并给出这类目标对并封闭的另一种证明。作为应用，作者首先证明 mean-payoff 目标在任意博弈图上具有位置策略；其次建立完备性结果：若目标 W 前缀无关、承认（弱）中性字母且在有限博弈图上具有位置策略，则存在 W'，它在有限博弈图上等价于 W，并在任意博弈图上具有位置策略。
We study the existence of positional strategies for the protagonist in infinite duration games over arbitrary game graphs. We prove that prefix-independent objectives in $Σ_0^2$ which are positional and admit a (strongly) neutral letter are exactly those that are recognised by history-deterministic monotone co-Bchi automata over countable ordinals. This generalises a criterion proposed by [Kopczyński, ICALP 2006] and gives an alternative proof of closure under union for these objectives, which was known from [Ohlmann, TheoretiCS 2023]. We then give two applications of our result. First, we prove that the mean-payoff objective is positional over arbitrary game graphs. Second, we establish the following completeness result: for any objective $W$ which is prefix-independent, admits a (weakly) neutral letter, and is positional over finite game graphs, there is an objective $W'$ which is equivalent to $W$ over finite game graphs and positional over arbitrary game graphs.
DOI 原文 · arXiv · PDF（开放获取） · DBLP
@article{OhlmannS26,
title = {Positionality in $Σ_0^2$ and a completeness result},
author = {Pierre Ohlmann and Michał Skrzypczak},
journal = {Logical Methods in Computer Science},
volume = {Volume 22, Issue 2},
year = {2026},
doi = {10.46298/lmcs-22(2:10)2026}
}