TY - JOUR

T1 - Seas of squares with sizes from a Π 1 0set

AU - Westrick, Linda Brown

N1 - Publisher Copyright:
© 2017, Hebrew University of Jerusalem.

PY - 2017/10/1

Y1 - 2017/10/1

N2 - 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.

AB - 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.

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U2 - 10.1007/s11856-017-1596-6

DO - 10.1007/s11856-017-1596-6

M3 - Article

AN - SCOPUS:85035028332

VL - 222

SP - 431

EP - 462

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

SN - 0021-2172

IS - 1

ER -