 The version of the theorem in Hedlund's paper applied only to one-dimensional finite automata, but a generalization to higher dimensional integer lattices was soon afterwards published by , and it can be even further generalized from lattices to discrete groups.One important consequence of the theorem is that, for reversible cellular automata, the reverse dynamics of the automaton can also be described by a cellular automaton.An alphabet is any finite set of symbols, which may be thought of as the states of the cells in a cellular automaton.