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A Theorem about the Algorithm of Minimization of Differences for Multicomponent Cellular Automata

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Cellular Automata (ACRI 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7495))

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Abstract

Multicomponent Cellular Automata, also known as Macroscopic Cellular Automata, characterize a methodological approach for modeling complex systems, that need many components both for the states (substates) to account for different properties of the cell and for the transition function (elementary processes) in order to account for various different dynamics. Many applications were developed for modeling complex natural phenomena, particularly macroscopic ones, e.g., large scale surface flows. Minimizing the differences of a certain quantity in the cell neighborhood, by distribution from the cell to the other neighboring cells, is a basic component of many transition functions in this context. The Algorithm for the Minimization of Differences (AMD) was applied in different ways to many models. A fundamental theorem about AMD is proved in this paper; it shows that AMD properties are more extended than the previous demonstrated theorem.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Calabria, Arcavacata, 87036, Rende, CS, Italy

    Maria Vittoria Avolio, Salvatore Di Gregorio & William Spataro

  2. DADU, University of Sassari, P. Duomo 6, 07041, Alghero, SS, Italy

    Giuseppe A. Trunfio

Authors
  1. Maria Vittoria Avolio
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  2. Salvatore Di Gregorio
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  3. William Spataro
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  4. Giuseppe A. Trunfio
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, Laboratory of Electronics, Democritus University of Thrace, GR 67100, Xanthi, Greece

    Georgios Ch. Sirakoulis

  2. CSAI - Complex Systems and Artificial Intelligence Research Center, University of Milano-Bicocca, 20134, Milano, Italy

    Stefania Bandini

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Avolio, M.V., Di Gregorio, S., Spataro, W., Trunfio, G.A. (2012). A Theorem about the Algorithm of Minimization of Differences for Multicomponent Cellular Automata. In: Sirakoulis, G.C., Bandini, S. (eds) Cellular Automata. ACRI 2012. Lecture Notes in Computer Science, vol 7495. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33350-7_30

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  • DOI: https://doi.org/10.1007/978-3-642-33350-7_30

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