如何为正则目标进行最优博弈？
How to Play Optimally for Regular Objectives?
AI总结：
本文研究图上双人零和博弈中正则目标的最优博弈记忆需求，获得了双方玩家色记忆需求的刻画，并证明判断是否存在足以最优博弈的小型记忆结构是 NP 完全的，部分结果适用于拓扑闭集和开集。
摘要：
本文研究图上的双人零和博弈，并对以下问题做出贡献：给定一个目标，为该目标进行最优博弈需要多少记忆？我们研究正则目标，其中一名玩家的目标是最终博弈路径上的颜色序列属于某种有限词的正则语言。我们获得了此类目标对双方玩家的色记忆需求的不同刻画，并由此推导出复杂性理论结论：对于双方玩家而言，判断是否存在足以进行最优博弈的小型记忆结构是 NP 完全的。我们的部分刻画结果适用于更广泛的目标类别：拓扑闭集和拓扑开集。
英文摘要：
This paper studies two-player zero-sum games played on graphs and makes contributions toward the following question: given an objective, how much memory is required to play optimally for that objective? We study regular objectives, where the goal of one of the two players is that eventually the sequence of colors along the play belongs to some regular language of finite words. We obtain different characterizations of the chromatic memory requirements for such objectives for both players, from which we derive complexity-theoretic statements: deciding whether there exist small memory structures sufficient to play optimally is NP-complete for both players. Some of our characterization results apply to a more general class of objectives: topologically closed and topologically open sets.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
