文章基本信息

标题：On the Expressive Power of Quasiperiodic SFT
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作者：Bruno Durand ; Andrei Romashchenko
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2017
卷号：83
页码：5:1-5:14
DOI：10.4230/LIPIcs.MFCS.2017.5
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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).
关键词：minimal SFT; tilings; quasiperiodicityIn this paper we study the shifts; which are the shift-invariant and topologically closed sets of configurations