2013/10/02 by Ville Salo, Salo, Ville, Ilkka Törmä +1
Computer Science · Mathematics · #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Formal Languages and Automata Theory (cs.FL) #Mathematical Dynamics and Fractals #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1310.0654
openalex publication_date 2013/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.