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This paper provides a brief summary of recent results on the number-conserving capabilities of cellular automata. We focus on studies that resulted in establishing complete lists of such CAs for a given dimension, state set, and neighborhood type. Moreover, we outline key, new questions arising from these results and point to obstacles hampering further progress.

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In Search of Cellular Automata that Preserve Numbers: Advances, Limitations, and Open Problems

  • 会议论文

  • 发表日期：

    2026年

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  • Barbara Wolnik,
  • Witold Bołt,
  • Bernard De Baets

摘要

This paper provides a brief summary of recent results on the number-conserving capabilities of cellular automata. We focus on studies that resulted in establishing complete lists of such CAs for a given dimension, state set, and neighborhood type. Moreover, we outline key, new questions arising from these results and point to obstacles hampering further progress.