We study three problems related to the computational complexity of the popular game Minesweeper. The first is consistency: given a set of clues, is there any arrangement of mines that satisfies it? This problem has been known to be NP-complete since 2000, but our framework proves it as a side effect. The second is inference: given a set of clues, is there any cell that the player can prove is safe? The coNP-completeness of this problem has been in the literature since 2011, but we discovered a flaw that we believe is present in all published results, and we provide a fixed proof. Finally, the third is solvability: given the full state of a Minesweeper game, can the player win the game by safely clicking all non-mine cells? This problem has not yet been studied, and we prove that it is coNP-complete.

翻译：我们研究了经典游戏扫雷的三个计算复杂度相关问题。第一个是一致性问题：给定一组线索，是否存在满足这些线索的地雷布局？该问题自2000年起已被证明是NP完全的，但我们的框架将其作为副产品进行了验证。第二个是推理问题：给定一组线索，玩家能否证明某个单元格是安全的？该问题的coNP完全性自2011年起便出现在文献中，但我们发现所有已发表结果中存在一个漏洞，并提供了修正后的证明。第三个是可解性问题：给定扫雷游戏的完整状态，玩家能否通过安全点击所有非地雷单元格获胜？该问题此前尚未被研究，我们证明其是coNP完全的。