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Suppose each site on a one-dimensional chain with periodic boundary condition may take on any one of the states 0, 1, . . . , n−1, can you find out the most frequently occurring state using cellular automaton? Here, we prove that while the above density classification task cannot be resolved by a single cellular automaton, this task can be performed efficiently by applying two cellular automaton rules in succession.

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Given a ͑finite but arbitrarily long͒ string of zeros and ones, we report a way to determine if the number of ones is less than, greater than, or equal to a prescribed number by applying two sets of cellular automaton rules in succession. Thus, we solve the general one-dimensional density classification problem using two cellular automata.

No abstract