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Reducing amount of possible states solving Pacman by searching

I consider simplified Pacman game: movement is discrete (on the grid), ghosts move deterministically based on difference between their and Pacmans coordinates, ghosts move every second turn, ghosts ...
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Whats the name of this search game?

I am struggling in finding the name of this game (in order to find research papers related to it in the literature). Given an initial word $X$ and a target word $Y$, what is the minimum number of (...