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Israel Journal of Mathematics

, Volume 222, Issue 1, pp 431–462 | Cite as

Seas of squares with sizes from a Π 1 0 set

  • Linda Brown Westrick
Article
  • 22 Downloads

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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© Hebrew University of Jerusalem 2017

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsVictoria University of WellingtonWellingtonNew Zealand

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