Positional games are a mathematical class of two-player games comprising Tic-tac-toe and its generalizations. We propose a novel encoding of these games into Quantified Boolean Formulas (QBF) such that a game instance admits a winning strategy for first player if and only if the corresponding formula is true. Our approach improves over previous QBF encodings of games in multiple ways. First, it is generic and lets us encode other positional games, such as Hex. Second, structural properties of positional games together with a careful treatment of illegal moves let us generate more compact instances that can be solved faster by state-of-the-art QBF solvers. We establish the latter fact through extensive experiments. Finally, the compactness of our new encoding makes it feasible to translate realistic game problems. We identify a few such problems of historical significance and put them forward to the QBF community as milestones of increasing difficulty.

中文翻译：

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位置游戏和 QBF：纠正编码

位置游戏是一种数学类的两人游戏，包括井字游戏及其推广。我们提出了将这些游戏编码为量化布尔公式 (QBF) 的新方法，这样当且仅当相应公式为真时，游戏实例才承认第一个玩家的获胜策略。我们的方法以多种方式改进了以前的游戏 QBF 编码。首先，它是通用的，让我们可以编码其他位置游戏，例如 Hex。其次，位置博弈的结构特性以及对非法移动的谨慎处理使我们能够生成更紧凑的实例，可以通过最先进的 QBF 求解器更快地求解。我们通过广泛的实验确定了后一个事实。最后，我们新编码的紧凑性使得翻译现实游戏问题成为可能。