Seas of squares with sizes from a Π 1 0set

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For each Π1 0S ⊆ 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 languageEnglish (US)
Pages (from-to)431-462
Number of pages32
JournalIsrael Journal of Mathematics
Issue number1
StatePublished - Oct 1 2017

All Science Journal Classification (ASJC) codes

  • General Mathematics


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