  We study algorithmic complexity of solving subtraction games in a~fixed
dimension with a finite difference set. We prove that there exists a game in
this class such that any algorithm solving the game runs in exponential time.
Also we prove an existence of a game in this class such that solving the game
is PSPACE-hard. The results are based on the construction introduced by Larsson
and W\"astlund. It relates subtraction games and cellular automata.
