一句话：给出图上安全目标策略所需最小记忆状态数的精确刻画：等于左商语言包含极大反链的大小。
本文研究图上双人博弈中保证安全目标的策略记忆需求，旨在给出策略所需最小记忆状态数的精确界。作者证明，该最小状态数恰好等于相对于语言包含关系的左商（left quotients）的最大反链大小。该刻画不依赖安全目标的任何正则性假设，因而适用于任意安全目标。基于这一一般原理，作者得到若干应用：精确刻画广义可达博弈中对手方所需的记忆；并证明带计数器博弈中存在位置策略。这些结果统一并推广了此前关于安全博弈记忆的界限。
We consider two-player games over graphs and give tight bounds on the memory size of strategies ensuring safety objectives. More specifically, we show that the minimal number of memory states of a strategy ensuring a safety objective is given by the size of the maximal antichain of left quotients with respect to language inclusion. This result holds for all safety objectives without any regularity assumptions. We give several applications of this general principle. In particular, we characterize the exact memory requirements for the opponent in generalized reachability games, and we prove the existence of positional strategies in games with counters.