The expressiveness of quasiperiodic and minimal shifts of finite type

Abstract

We study multidimensional minimal and quasiperiodic shifts of finite type. We prove for these classes several results that were previously known for the shifts of finite type in general, without restriction. We show that some quasiperiodic shifts of finite type admit only non-computable configurations; we characterize the classes of Turing degrees that can be represented by quasiperiodic shifts of finite type. We also transpose to the classes of minimal/quasiperiodic shifts of finite type some results on subdynamics previously known for the effective shifts without restrictions: every effective minimal (quasiperiodic) shift of dimension $d$ can be represented as a projection of a subdynamics of a minimal (respectively, quasiperiodic) shift of finite type of dimension $d+1$.

60 pages, 23 figures. Preliminary versions of some of the presented results was published in conference papers on MFCS2015 [see arXiv:1504.06130] and MFCS2017 [see arXiv:1705.01876]. Accepted to the ETDS journal (Nov. 2019)

References in corpus (3)

• Simulation of Effective Subshifts by Two-dimensional Subshifts of Finite Type
• A self-similar aperiodic set of 19 Wang tiles
• Quantified block gluing, aperiodicity and entropy of multidimensional SFT