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Rectangular tileability and complementary tileability are undecidable (1212.3380v1)
Published 14 Dec 2012 in math.CO, cs.CC, and cs.CG
Abstract: Does a given a set of polyominoes tile some rectangle? We show that this problem is undecidable. In a different direction, we also consider tiling a cofinite subset of the plane. The tileability is undecidable for many variants of this problem. However, we present an algorithm for testing whether the complement of a finite region is tileable by a set of rectangles.