Generalized Chat Noir is PSPACE-Complete

摘要

We study the computational complexity of the following two-player game. The instance is a graph G = (V, E), an initial vertex s s V, and a target set T Q V. A "cat" is initially placed on s. Player 1 chooses a vertex in the graph and removes it and its incident edges from the graph. Player 2 moves the cat from the current vertex to one of the adjacent vertices. Players 1 and 2 alternate removing a vertex and moving the cat, respectively. The game continues until either the cat reaches a vertex of T or the cat cannot be moved. Player 1 wins if and only if the cat cannot be moved before it reaches a vertex of T. It is shown that deciding whether player 1 has a forced win on the game on G is PSPACE-complete.