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Affine continuous cellular automata solving the fixed-length density classification problem

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Abstract

In this paper, the classical density classification problem is considered in the context of affine continuous cellular automata. It has been shown earlier that there exists no general solution to this problem that is valid for any number of cells. Here, we consider this problem in the case of a fixed number of cells. Necessary conditions for solving the problem are formulated. Based on this knowledge, a specific class of affine continuous cellular automata is evaluated experimentally for 23 cells. A rich solution set is analysed and visualised.

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Acknowledgements

Computations were carried out at the Academic Computer Centre in Gdańsk (TASK KDM). Witold Bołt is supported by the Foundation for Polish Science under International PhD Projects in Intelligent Computing. This project is financed by the European Union within the Innovative Economy Operational Program 2007–2013 and the European Regional Development Fund.

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Authors and Affiliations

  1. Institute of Mathematics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, 80-308, Gdańsk, Poland

    Marcin Dembowski & Barbara Wolnik

  2. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Witold Bołt

  3. KERMIT, Department of Mathematical Modelling, Statistics and Bioinformatics, Ghent University, Ghent, Belgium

    Witold Bołt, Jan M. Baetens & Bernard De Baets

Authors
  1. Marcin Dembowski
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  2. Barbara Wolnik
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  3. Witold Bołt
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  4. Jan M. Baetens
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  5. Bernard De Baets
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Correspondence to Marcin Dembowski.

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Dembowski, M., Wolnik, B., Bołt, W. et al. Affine continuous cellular automata solving the fixed-length density classification problem. Nat Comput 17, 467–477 (2018). https://doi.org/10.1007/s11047-017-9631-4

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  • DOI: https://doi.org/10.1007/s11047-017-9631-4

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