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Cellular automata universality revisited

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Fundamentals of Computation Theory (FCT 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1279))

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Abstract

We propose an original arithmetization of cellular automata independent of Turing machines and present a new classification of universal cellular automata according to the way universality is achieved. Indeed, there are many possibilities to get the universality of cellular automata all based on simulations. Consider, for instance the simulation of any other cellular automaton or the simulation of a given universal Turing machine. The two simulations are quite different but both lead to the construction of a universal cellular automaton. We will distinguish three different simulations. The three kinds of corresponding universal machines are defined as simulation-universal, hereditary-universal and construction-universal. As an illustration, we propose an alternative definition of Kolmogorov complexity. We also recall an undecidability result and a well-known complexity result. The last two results hold as soon as we have a hereditary-universal machine.

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Authors and Affiliations

  1. Laboratoire I3S-UPRES-A 6070, Université de Nice Sophia-Antipolis, 930 Route des Colles, BP 145, F-06903, Sophia-Antipolis Cedex, France

    Bruno Martin

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  1. Bruno Martin
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Bogdan S. Chlebus Ludwik Czaja

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© 1997 Springer-Verlag Berlin Heidelberg

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Martin, B. (1997). Cellular automata universality revisited. In: Chlebus, B.S., Czaja, L. (eds) Fundamentals of Computation Theory. FCT 1997. Lecture Notes in Computer Science, vol 1279. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0036195

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  • DOI: https://doi.org/10.1007/BFb0036195

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63386-0

  • Online ISBN: 978-3-540-69529-5

  • eBook Packages: Springer Book Archive

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