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Additive cellular automata over ℤp and the bottom of (CA,≤)

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Mathematical Foundations of Computer Science 1998 (MFCS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1450))

Abstract

In a previous work we began to study the question of “how to compare” cellular automata (CA). In that context it was introduced a preorder (CA,≤) admitting a global minimum and it was shown that all the CA satisfying very simple dynamical properties as nilpotency or periodicity are located “on the bottom of (CA,≤)”. Here we prove that also the (algebraically amenable) additive CA over ℤ p are located on the bottom of (CA,≤). This result encourages our conjecture that says that the “distance” from the minimum could represent a measure of “complexity” on CA. We also prove that the additive CA over ℤ p with p prime are pairwise incomparable. This fact improves our understanding of (CA,≤) because it means that the minimum, even in the canonical order compatible with ≤, has infinite outdegree.

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Luboš Brim Jozef Gruska Jiří Zlatuška

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© 1998 Springer-Verlag Berlin Heidelberg

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Mazoyer, J., Rapaport, I. (1998). Additive cellular automata over ℤp and the bottom of (CA,≤). In: Brim, L., Gruska, J., Zlatuška, J. (eds) Mathematical Foundations of Computer Science 1998. MFCS 1998. Lecture Notes in Computer Science, vol 1450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055835

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  • DOI: https://doi.org/10.1007/BFb0055835

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64827-7

  • Online ISBN: 978-3-540-68532-6

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