Constructions with Countable Subshifts of Finite Type

: Ville Salo, Ilkka Törmä

Publisher: IOS Press

: 2013

: Fundamenta Informaticae

: FI

: 8

: 2-3

: 126

: 2-3

: 263

: 300

: 38

: 1875-8681

DOI: https://doi.org/10.3233/FI-2013-881

We present constructions of countable two-dimensional subshifts of finite type (SFTs) with interesting properties. Our main focus is on properties of the topological derivatives and subpattern posets of these objects. We present a countable SFT whose iterated derivatives are maximally complex from the computational point of view, constructions of countable SFTs with high Cantor-Bendixson ranks, a countable SFT whose subpattern poset contains an infinite descending chain and a countable SFT whose subpattern poset contains all finite posets. When possible, we make these constructions deterministic, and ensure the sets of rows are very simple as one-dimensional subshifts.

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