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Non-uniform number-conserving elementary cellular automata on the infinite grid : a tale of the unexpected

Barbara Wolnik (UGent) , Maciej Dziemiańczuk and Bernard De Baets (UGent)
(2023) INFORMATION SCIENCES. 649.
Author
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Abstract
In this paper, we study non-uniform elementary cellular automata on the infinite grid in the context of number conservation. These automata operate in a one-dimensional setting, where individual cells can employ distinct Wolfram rules for updating their states. The result is an exhaustive characterization of such number-conserving cellular automata. Until now, such a characterization was known only for finite grids, for which research hypotheses could be derived on the basis of computer experiments. It turns out that when considering number conservation for non-uniform cellular automata, the infinite grid cannot be treated as a limiting case of finite grids, i.e., there are number-conserving non-uniform cellular automata on the infinite grid that have no analogous counterpart on finite grids.
Keywords
Artificial Intelligence, Information Systems and Management, Computer Science Applications, Theoretical Computer Science, Control and Systems Engineering, Software

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MLA
Wolnik, Barbara, et al. “Non-Uniform Number-Conserving Elementary Cellular Automata on the Infinite Grid : A Tale of the Unexpected.” INFORMATION SCIENCES, vol. 649, 2023, doi:10.1016/j.ins.2023.119680.
APA
Wolnik, B., Dziemiańczuk, M., & De Baets, B. (2023). Non-uniform number-conserving elementary cellular automata on the infinite grid : a tale of the unexpected. INFORMATION SCIENCES, 649. https://doi.org/10.1016/j.ins.2023.119680
Chicago author-date
Wolnik, Barbara, Maciej Dziemiańczuk, and Bernard De Baets. 2023. “Non-Uniform Number-Conserving Elementary Cellular Automata on the Infinite Grid : A Tale of the Unexpected.” INFORMATION SCIENCES 649. https://doi.org/10.1016/j.ins.2023.119680.
Chicago author-date (all authors)
Wolnik, Barbara, Maciej Dziemiańczuk, and Bernard De Baets. 2023. “Non-Uniform Number-Conserving Elementary Cellular Automata on the Infinite Grid : A Tale of the Unexpected.” INFORMATION SCIENCES 649. doi:10.1016/j.ins.2023.119680.
Vancouver
1.
Wolnik B, Dziemiańczuk M, De Baets B. Non-uniform number-conserving elementary cellular automata on the infinite grid : a tale of the unexpected. INFORMATION SCIENCES. 2023;649.
IEEE
[1]
B. Wolnik, M. Dziemiańczuk, and B. De Baets, “Non-uniform number-conserving elementary cellular automata on the infinite grid : a tale of the unexpected,” INFORMATION SCIENCES, vol. 649, 2023.
@article{01HAKPYPN3YB92HAKA3DQQBH1H,
  abstract     = {{In this paper, we study non-uniform elementary cellular automata on the infinite grid in the context of number conservation. These automata operate in a one-dimensional setting, where individual cells can employ distinct Wolfram rules for updating their states. The result is an exhaustive characterization of such number-conserving cellular automata. Until now, such a characterization was known only for finite grids, for which research hypotheses could be derived on the basis of computer experiments. It turns out that when considering number conservation for non-uniform cellular automata, the infinite grid cannot be treated as a limiting case of finite grids, i.e., there are number-conserving non-uniform cellular automata on the infinite grid that have no analogous counterpart on finite grids.}},
  articleno    = {{119680}},
  author       = {{Wolnik, Barbara and Dziemiańczuk, Maciej and De Baets, Bernard}},
  issn         = {{0020-0255}},
  journal      = {{INFORMATION SCIENCES}},
  keywords     = {{Artificial Intelligence,Information Systems and Management,Computer Science Applications,Theoretical Computer Science,Control and Systems Engineering,Software}},
  language     = {{eng}},
  pages        = {{13}},
  title        = {{Non-uniform number-conserving elementary cellular automata on the infinite grid : a tale of the unexpected}},
  url          = {{http://doi.org/10.1016/j.ins.2023.119680}},
  volume       = {{649}},
  year         = {{2023}},
}
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