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We study the computational complexity of determining whether a cellular automaton is sensitive to initial conditions. We show that this problem is \(\varPi ^0_2\) -complete in dimension 1 and \(\varSigma ^0_3\) -complete in dimension 2 and higher. This solves a question posed by Sablik and Theyssier.

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Descriptive Complexity of Sensitivity of Cellular Automata

  • 会议论文

  • 发表日期：

    2026年

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  • Tom Favereau,
  • Ville Salo

摘要

We study the computational complexity of determining whether a cellular automaton is sensitive to initial conditions. We show that this problem is \(\varPi ^0_2\) -complete in dimension 1 and \(\varSigma ^0_3\) -complete in dimension 2 and higher. This solves a question posed by Sablik and Theyssier.