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Computation theory of cellular automata

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Abstract

Self-organizing behaviour in cellular automata is discussed as a computational process. Formal language theory is used to extend dynamical systems theory descriptions of cellular automata. The sets of configurations generated after a finite number of time steps of cellular automaton evolution are shown to form regular languages. Many examples are given. The sizes of the minimal grammars for these languages provide measures of the complexities of the sets. This complexity is usually found to be non-decreasing with time. The limit sets generated by some classes of cellular automata correspond to regular languages. For other classes of cellular automata they appear to correspond to more complicated languages. Many properties of these sets are then formally non-computable. It is suggested that such undecidability is common in these and other dynamical systems.

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Authors and Affiliations

  1. The Institute for Advanced Study, 08540, Princeton, NJ, USA

    Stephen Wolfram

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  1. Stephen Wolfram
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Additional information

Communicated by O. E. Lanford

Work supported in part by the U.S. Office of Naval Research under contract number N 00014-80-C-0657

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Wolfram, S. Computation theory of cellular automata. Commun.Math. Phys. 96, 15–57 (1984). https://doi.org/10.1007/BF01217347

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  • DOI: https://doi.org/10.1007/BF01217347

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