Computability of Countable Subshifts
نویسندگان
چکیده
The computability of countable subshifts and their members is examined. Results include the following. Subshifts of CantorBendixson rank one contain only eventually periodic elements. Any rank one subshift, in which every limit point is periodic, is decidable. Subshifts of rank two may contain members of arbitrary Turing degree. In contrast, effectively closed (Π 1 ) subshifts of rank two contain only computable elements, but Π 1 subshifts of rank three may contain members of arbitrary c. e. degree. There is no subshift of rank ω.
منابع مشابه
Structuring multi-dimensional subshifts
We study two relations on multi-dimensional subshifts: A pre-order based on the patterns configurations contain and the Cantor-Bendixson rank. We exhibit several structural properties of two-dimensional subshifts: We characterize the simplest aperiodic configurations in countable SFTs, we give a combinatorial characterization of uncountable subshifts, we prove that there always exists configura...
متن کاملConstructions with Countable Subshifts of Finite Type
We present constructions of countable two-dimensional subshifts of finite type (SFTs) with interesting properties. Our main focus is on properties of the topological derivatives and subpattern posets of these objects. We present a countable SFT whose iterated derivatives are maximally complex from the computational point of view, constructions of countable SFTs with high CantorBendixson ranks, ...
متن کاملComputing the entropy of one-dimensional decidable subshifts
We characterise the difficulty of computing topological entropy of one-dimensional subshifts under various dynamical restrictions. Entropy is known to be computable from above for general one-dimensional subshifts, and the aim of the article is to distinguish under which dynamical properties it becomes computable. The considered properties are minimality, unique ergodicity, and various forms of...
متن کاملOn Derivatives and Subpattern Orders of Countable Subshifts
We study the computational and structural aspects of countable two-dimensional SFTs and other subshifts. Our main focus is on the topological derivatives and subpattern posets of these objects, and our main results are constructions of two-dimensional countable subshifts with interesting properties. We present an SFT whose iterated derivatives are maximally complex from the computational point ...
متن کاملPresentations of Symbolic Dynamical Systems by Labelled Directed Graphs (notes for a ”mini-cours”, Sda2, Paris 4-5 October 2007)
We develop some aspects of a general theory of presentations of subshifts by labelled directed graphs, in particular by compact graphs. Also considered are synchronization properties of subshifts that lead to presentations by countable graphs. Let Σ be a finite alphabet. In symbolic dynamics one studies subshifts (X,SX), X a shift-invariant closed subset of the shift space Σ Z and SX the restri...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010