Abstract
Totalistic cellular automata, introduced by S. Wolfram, are cellular automata in which the state transition function depends only on the sum of the states in a cell's neighborhood. Each state is considered as a nonnegative integer and the sum includes the cell's own state. It is shown that one-dimensional totalistic cellular automata can simulate an arbitrary Turing machine in linear time, even when the neighborhood is restricted to one cell on each side. This result settles Wolfram's conjecture that totalistic cellular automata are computation-universal.
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Research performed while visiting the Department of Computer Science, University of Cincinnati, 1984/85.
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Gordon, D. On the computational power of totalistic cellular automata. Math. Systems Theory 20, 43–52 (1987). https://doi.org/10.1007/BF01692058
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DOI: https://doi.org/10.1007/BF01692058