A4 Refereed article in a conference publication
On Derivatives and Subpattern Orders of Countable Subshifts
Authors: Ville Salo, Ilkka Törmä
Editors: Enrico Formenti
Publication year: 2012
Journal: Electronic Proceedings in Theoretical Computer Science
Book title : Proceedings 18th international workshop on Cellular Automata and Discrete Complex Systems and 3rd international symposium Journées Automates Cellulaires
Series title: Electronic Proceedings in Theoretical Computer Science
First page : 23
Last page: 36
ISSN: 2075-2180
DOI: https://doi.org/10.4204/EPTCS.90.3(external)
Abstract
We study the computational and structural aspects of countable two-dimensional SFTs and other subshifts. Our main focus is on the topological derivatives and subpattern posets of these objects, and our main results are constructions of two-dimensional countable subshifts with interesting properties. We present an SFT whose iterated derivatives are maximally complex from the computational point of view, a sofic shift whose subpattern poset contains an infinite descending chain, a family of SFTs whose finite subpattern posets contain arbitrary finite posets, and a natural example of an SFT with infinite Cantor-Bendixon rank.
We study the computational and structural aspects of countable two-dimensional SFTs and other subshifts. Our main focus is on the topological derivatives and subpattern posets of these objects, and our main results are constructions of two-dimensional countable subshifts with interesting properties. We present an SFT whose iterated derivatives are maximally complex from the computational point of view, a sofic shift whose subpattern poset contains an infinite descending chain, a family of SFTs whose finite subpattern posets contain arbitrary finite posets, and a natural example of an SFT with infinite Cantor-Bendixon rank.
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