Impartial games emulating one-dimensional cellular automata and undecidability
Journal article, 2013

We study two-player impartial 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 rule 110 games.

Undecidability

Take-away game

Impartial game

Cellular automaton

Rule 110

Author

Urban Larsson

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Journal of Combinatorial Theory - Series A

0097-3165 (ISSN)

Vol. 120 5 1116-1130

Subject Categories

Mathematics

Discrete Mathematics

DOI

10.1016/j.jcta.2013.02.009

More information

Created

10/6/2017