Growth-type invariants for ℤ^d subshifts of finite type and classes arithmetical of real numbers

2009/02/02 by Tom Meyerovitch, Meyerovitch, Tom
Computer Science · Mathematics · #03D55 #03D80 #37B10 #37B50 #52C23 #Algorithms and Data Compression #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Logic (math.LO) #Mathematical Dynamics and Fractals #math.DS #math.LO #msc:03D55 #msc:03D80 #msc:37B10 #msc:37B50 #msc:52C23

paper · pdf · doi:10.48550/arxiv.0902.0223

17 pages, 2 figures

arxiv created 2009/02/02 · openalex publication_date 2009/02/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss some numerical invariants of multidimensional shifts of finite type (SFTs) which are associated with the growth rates of the number of admissible finite configurations. Extending an unpublished example of Tsirelson, we show that growth complexities of the form exp(n^α) are possible for non-integer α's. In terminology of Carvalho, such subshifts have entropy dimension α. The class of possible α's are identified in terms of arithmetical classes of real numbers of Weihrauch and Zheng.

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