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The Mirage of Universality in Cellular Automata

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Part of the Emergence, Complexity and Computation book series (ECC,volume 42)

Abstract

This note is a survey of examples and results about cellular automata with the purpose of recalling that there is no ‘universal’ way of being computationally universal. In particular, we show how some cellular automata can embed efficient but bounded computation, while others can embed unbounded computations but not efficiently. We also study two variants of Boolean circuit embedding, transient versus repeatable simulations, and underline their differences. Finally we show how strong forms of universality can be hidden inside some seemingly simple cellular automata according to some classical dynamical parameters.

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  • DOI: 10.1007/978-3-030-92551-2_5
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Fig. 1
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Notes

  1. 1.

    It should be noted however that a growing trend in symbolic dynamics has shown the importance of computability considerations. Some of these results were even published in real math journals.

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Correspondence to Guillaume Theyssier .

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Theyssier, G. (2022). The Mirage of Universality in Cellular Automata. In: Adamatzky, A. (eds) Automata and Complexity. Emergence, Complexity and Computation, vol 42. Springer, Cham. https://doi.org/10.1007/978-3-030-92551-2_5

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  • DOI: https://doi.org/10.1007/978-3-030-92551-2_5

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