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Handbook of Natural Computing pp 189–229Cite as

Universalities in Cellular Automata*

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Abstract

This chapter is dedicated to computational universalities in cellular automata, essentially Turing universality, the ability to compute any recursive function, and intrinsic universality, the ability to simulate any other cellular automaton. Constructions of Boolean circuits simulation in the two-dimensional case are explained in detail to achieve both kinds of universality. A detailed chronology of seminal papers is given, followed by a brief discussion of the formalization of universalities. The more difficult one-dimensional case is then discussed. Seminal universal cellular automata and encoding techniques are presented in both dimensions.

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Notes

  1. 1.

    *A preliminary version of this work appeared under the title Universalities in Cellular Automata: A (Short) Survey in the proceedings of the first edition of the JAC conference (Ollinger 2008).

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Acknowledgment

The author would like to thank G. Richard for providing and preparing figures to illustrate both rule 110 and the 4-state intrinsically universal cellular automaton.

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Authors and Affiliations

  1. Laboratoire d'informatique fondamentale de Marseille (LIF), Aix-Marseille Université, CNRS, Marseille, France

    Nicolas Ollinger

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  1. Nicolas Ollinger
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Editors and Affiliations

  1. LIACS, Leiden University, Leiden, The Netherlands

    Grzegorz Rozenberg

  2. Computer Science Department, University of Colorado, Boulder, USA

    Grzegorz Rozenberg

  3. LIACS, Leiden University, Leiden, The Netherlands

    Thomas Bäck

  4. LIACS, Leiden University, Leiden, The Netherlands

    Joost N. Kok

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Ollinger, N. (2012). Universalities in Cellular Automata*. In: Rozenberg, G., Bäck, T., Kok, J.N. (eds) Handbook of Natural Computing. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92910-9_6

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