与记忆有限的对手比赛
Playing Against Opponents With Limited Memory
摘要：
研究了图上目标为Ω-正则目标的\emph{partial-information}回合制二人博弈，其中部分信息局中人具有\emph{limited memory} .这样的游戏是一个自然的形式化反应合成时，环境的球员是不是真正的对抗系统的球员。环境玩家有自己的目标，但环境玩家的确切目标对系统玩家来说是未知的。我们证明了确定系统玩家的获胜策略的存在性的问题是PSPACE难的可达性，安全性和奇偶性目标。此外，当环境播放器是无记忆的时，问题是PSPACE完全的。然而，决定环境参与者是否有获胜策略更简单;它只是NP完全的。此外，我们构建了一个游戏，部分信息的球员需要至少$\mathcal{O}(\sqrt{n})$位的内存，以保持在游戏中的大小$\mathcal{O}(n)$获胜的策略。
英文摘要：
We study \emph{partial-information} two-player turn-based games on graphs with omega-regular objectives, when the partial-information player has \emph{limited memory}. Such games are a natural formalization for reactive synthesis when the environment player is not genuinely adversarial to the system player. The environment player has goals of its own, but the exact goal of the environment player is unknown to the system player. We prove that the problem of determining the existence of a winning strategy for the system player is PSPACE-hard for reachability, safety, and parity objectives. Moreover, when the environment player is memoryless, the problem is PSPACE-complete. However, it is simpler to decide if the environment player has a winning strategy; it is only NP-complete. Additionally, we construct a game where the the partial-information player needs at least $\mathcal{O}(\sqrt{n})$ bits of memory to retain winning strategies in a game of size $\mathcal{O}(n)$.
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。
