The 4-way deterministic tiling problem is undecidable

Authors:
Ville Lukkarila
Affiliations:
Department of Mathematics, University of Turku, FI-20014 Turku, Finland and Turku Centre for Computer Science, FI-20520 Turku, Finland
Venue:
Theoretical Computer Science
Year:
2009

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Abstract

It is shown that the (infinite) tiling problem by Wang tiles is undecidable even if the given tile set is deterministic by all four corners, i.e. a tile is uniquely determined by the colors of any two adjacent edges. The reduction is done from the Turing machine halting problem and uses the aperiodic tile set of Kari and Papasoglu.