## Abstract

For each Π_{1} ^{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.

Original language | English (US) |
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Pages (from-to) | 431-462 |

Number of pages | 32 |

Journal | Israel Journal of Mathematics |

Volume | 222 |

Issue number | 1 |

DOIs | |

State | Published - Oct 1 2017 |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)

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