Impartial games emulating one-dimensional cellular automata and undecidability
Combinatorics
2012-01-06 v1 Information Theory
math.IT
Cellular Automata and Lattice Gases
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.
Keywords
Cite
@article{arxiv.1201.1039,
title = {Impartial games emulating one-dimensional cellular automata and undecidability},
author = {Urban Larsson},
journal= {arXiv preprint arXiv:1201.1039},
year = {2012}
}
Comments
22 pages, 11 figures