On Derivatives and Subpattern Orders of Countable Subshifts



: Ville Salo, Ilkka Törmä

: Enrico Formenti

: 2012

: Electronic Proceedings in Theoretical Computer Science

: Proceedings 18th international workshop on Cellular Automata and Discrete Complex Systems and 3rd international symposium Journées Automates Cellulaires

: Electronic Proceedings in Theoretical Computer Science

: 23

: 36

: 2075-2180

DOI: https://doi.org/10.4204/EPTCS.90.3


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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