Impartial games emulating one-dimensional cellular automata and undecidability

Details Impartial games emulating one-dimensional cellular automata and undecidability Impartial games emulating one-dimensional cellular automata and undecidability

2012-01-05

arxiv.org/abs/1201.1039v1

Mathematics

Combinatorics

22 pages, 11 figures

Scientific paper

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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