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arXiv · 1201.1039

Impartial games emulating one-dimensional cellular automata and undecidability

Urban Larsson
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Abstract

We study two-player \emph{take-away} games whose outcomes emulate two-state one-dimensional cellular automata, such as Wolfram's rules 60 and 110. Given an initial string consisting of a central data pattern and periodic left and right patterns, the rule 110 cellular automaton was recently proved Turing-complete by Matthew Cook. Hence, many questions regarding its behavior are algorithmically undecidable. We show that similar questions are undecidable for our \emph{rule 110} game.

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Urban Larsson. 2012-01-05. Impartial games emulating one-dimensional cellular automata and undecidability. https://arxiv.org/abs/1201.1039

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