The paper studies the computational complexity of three decision problems related to the popular game Minesweeper:
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.
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 the authors discovered a flaw in the existing proofs and provide a fixed proof.
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 the authors prove that it is coNP-complete.
The authors develop a framework based on graph orientation to prove the hardness results. They define three related graph orientation decision problems (consistency, promise-inference, and uniqueness) and show that each is hard using a particular set of simple abstract gadgets. They then apply this framework to Minesweeper and many variants, showing that finding well-behaved constructions in Minesweeper that behave like the abstract gadgets is enough to prove hardness for all three Minesweeper problems.
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