Two-Player Games on Cellular Automata

Cellular automata games have traditionally been solitaire games. We define a two-player cellular automata game played on a finite cyclic digraph G = (V,E). Each vertex assumes a weight w I {0,1}. A move consists of selecting a vertex u with w(u) = 1 and firing it, i.e., complementing its weight and that of a selected neighborhood of u. The player first making all weights 0 wins, and the opponent loses. If there is no last move, the outcome is a draw. The main part of the paper consists of constructing a polynomial strategy. The 3-fold motivation for exploring these games stems from complexity considerations in combinatorial game theory, transforming the hitherto solitaire cellular automata games into two-player games, and the theory of linear error correcting codes.

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