cat & mice on chessboard riddle


Four white pieces (the mice) are placed on one side of a chessboard, and one black piece (the cat) is placed at the opposite side. The game is played by the following rules:

black wins if it reaches the opposite side;
white wins if it blocks black in such a way that black cannot make any move anymore;
only diagonal moves (of length 1) on empty squares are allowed;
white only moves forward;
black can move backward and forward;
black may make the first move, then white makes a move, and so on.

Is this game computable (i.e. is it possible to decide beforehand who wins the game, no matter how hard his opponent tries to avoid this)?

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