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On the Expressive Power of Quasiperiodic SFT Durand, Bruno Romashchenko, Andrei minimal SFT tilings quasiperiodicityIn this paper we study the shifts which are the shift-invariant and topologically closed sets of configurations In this paper we study the shifts, which are the shift-invariant and topologically closed sets of configurations over a finite alphabet in Z^d. The minimal shifts are those shifts in which all configurations contain exactly the same patterns. Two classes of shifts play a prominent role in symbolic dynamics, in language theory and in the theory of computability: the shifts of finite type (obtained by forbidding a finite number of finite patterns) and the effective shifts (obtained by forbidding a computably enumerable set of finite patterns). We prove that every effective minimal shift can be represented as a factor of a projective subdynamics on a minimal shift of finite type in a bigger (by 1) dimension. This result transfers to the class of minimal shifts a theorem by M.Hochman known for the class of all effective shifts and thus answers an open question by E. Jeandel. We prove a similar result for quasiperiodic shifts and also show that there exists a quasiperiodic shift of finite type for which Kolmogorov complexity of all patterns of size n\times n is \Omega(n). Schloss Dagstuhl – Leibniz-Zentrum für Informatik Bruno Durand and Andrei Romashchenko 2017 Is Part Of LIPIcs, Volume 83, 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.MFCS.2017.5 urn:nbn:de:0030-drops-80985 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.5 eng https://creativecommons.org/licenses/by/3.0/legalcode