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Seas of squares with sizes from a Π 01 set

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Abstract

For each Π1 0 S ⊆ N, let the S-square shift be the two-dimensional subshift on the alphabet {0, 1} whose elements consist of squares of 1s of various sizes on a background of 0s, where the side length of each square is in S. Similarly, let the distinct-square shift consist of seas of squares such that no two finite squares have the same size. Extending the self-similar Turing machine tiling construction of [6], we show that if X is an S-square shift or any effectively closed subshift of the distinct square shift, then X is sofic.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Victoria University of Wellington, PO Box 600, Wellington, 6140, New Zealand

    Linda Brown Westrick

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  1. Linda Brown Westrick
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Correspondence to Linda Brown Westrick.

Additional information

The author was supported by Noam Greenberg’s Rutherford Discovery Fellowship as a postdoctoral fellow.

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Westrick, L.B. Seas of squares with sizes from a Π 01 set. Isr. J. Math. 222, 431–462 (2017). https://doi.org/10.1007/s11856-017-1596-6

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  • DOI: https://doi.org/10.1007/s11856-017-1596-6

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