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Inducing an order on cellular automata by a grouping operation

  • Automata and Formal Languages I
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STACS 98 (STACS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1373))

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Abstract

A grouped instance of a cellular automaton (CA) is another one obtained by grouping several states into blocks and by letting interact neighbor blocks. Based on this operation a preorder ≤ on the set of one dimensional CA is introduced. It is shown that (CA,≤) admits a global minimum and that on the bottom of (CA,≤) very natural equivalence classes are located. These classes remind us the first two well-known Wolfram ones because they capture global (or dynamical) properties as nilpotency or periodicity. Non trivial properties as the undecidability of ≤ and the existence of bounded infinite chains are also proved. Finally, it is shown that (CA,≤) admits no maximum. This result allows us to conclude that, in a “grouping sense”, there is no universal CA.

This work was partially supported by Program ECOS-97.

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Authors and Affiliations

  1. LIP-École Normale Supérieure Supérieure de Lyon, 46 Allée d'Italie, 69364, Lyon Cedex 07, France

    Jacques Mazoyer & Ivan Rapaport

Authors
  1. Jacques Mazoyer
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  2. Ivan Rapaport
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Michel Morvan Christoph Meinel Daniel Krob

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© 1998 Springer-Verlag

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Mazoyer, J., Rapaport, I. (1998). Inducing an order on cellular automata by a grouping operation. In: Morvan, M., Meinel, C., Krob, D. (eds) STACS 98. STACS 1998. Lecture Notes in Computer Science, vol 1373. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028554

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  • DOI: https://doi.org/10.1007/BFb0028554

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64230-5

  • Online ISBN: 978-3-540-69705-3

  • eBook Packages: Springer Book Archive

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