A1 Refereed original research article in a scientific journal
Constructions with Countable Subshifts of Finite Type
Authors: Ville Salo, Ilkka Törmä
Publisher: IOS Press
Publication year: 2013
Journal: Fundamenta Informaticae
Journal acronym: FI
Article number: 8
Number in series: 2-3
Volume: 126
Issue: 2-3
First page : 263
Last page: 300
Number of pages: 38
ISSN: 1875-8681
eISSN: 1875-8681
DOI: https://doi.org/10.3233/FI-2013-881
Abstract
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.
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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