2×n Minesweeper Consistency Problem is in P

Abstract

Minesweeper is a popular single-player game included with Windows operating systems. Since Richard Kaye [12] proved that “Minesweeper is NP-complete” in 2000, it has been recently studied by many researchers. Meredith Kadlac [7] had showed that one-dimensional Minesweeper consistency problem is regular and can be recognized by a deterministic finite automaton. We extend the consistency problem to 2×n Minesweeper, which is two-dimensional but with its one dimension restricted to 2. We find that this problem is also tractable and design a finite automaton which can solve 2×n Minesweeper consistency problem in linear time. Hence, we are able to show that 2×n Minesweeper consistency problem is also in P.