Subshifts with sparse traces

2016/05/31 by Ville Salo, Salo, Ville · 2 citations
Computer Science · Mathematics · #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1605.09623

openalex publication_date 2016/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study two-dimensional subshifts whose horizontal trace (a.k.a. projective subdynamics) contains only points of finite support. Our main result is a classification result for such subshifts satisfying a minimality property. As corollaries, we obtain new proofs for various known results on traces of SFTs, nilpotency and decidability of cellular automata, topological full groups and the subshift of prime numbers. We also construct various (sofic) examples illustrating the concepts.

Citations

• The undecidability of the domino problem

Cited by

• A Three-Dimensional SFT with Sparse Columns
• Flows with minimal subdynamics

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