The Complexity of the Topological Conjugacy Problem for Toeplitz Subshifts
نویسنده
چکیده
In this paper, we analyze the Borel complexity of the topological conjugacy relation on Toeplitz subshifts. More specifically, we prove that topological conjugacy of Toeplitz subshifts with separated holes is hyperfinite. Indeed, we show that the topological conjugacy relation is hyperfinite on a larger class of Toeplitz subshifts which we call Toeplitz subshifts with growing blocks. This result provides a partial answer to a question asked by Sabok and Tsankov.
منابع مشابه
Algorithmic Complexity for the Realization of an Effective Subshift By a Sofic
Realization of d-dimensional effective subshifts as projective sub-actions of d + d′-dimensional sofic subshifts for d′ ≥ 1 is now well known [6, 4, 2]. In this paper we are interested in qualitative aspects of this realization. We introduce a new topological conjugacy invariant for effective subshifts, the speed of convergence, in view to exhibit algorithmic properties of these subshifts in co...
متن کاملA Matrix Formalism for Conjugacies of Higher-dimensional Shifts of Finite Type
We develop a natural matrix formalism for state splittings and amalgamations of higher-dimensional subshifts of finite type which extends the common notion of strong shift equivalence of Z+-matrices. Using the decomposition theorem every topological conjugacy between two Zd-shifts of finite type can thus be factorized into a finite chain of matrix transformations acting on the transition matric...
متن کاملDynamically Deened Recurrence Dimension
In this paper, we introduce and characterize the dynamically deened recurrence dimension, a new topological invariant number, following the idea of a previous article 9], but with some modiications and improvements. We study some example of Toeplitz subshifts for which we can show that the recurrence dimension is a topologically invariant number diierent from the topological entropy.
متن کاملHardness of conjugacy and factorization of multidimensional subshifts of finite type
We investigate here the hardness of conjugacy and factorization of subshifts of finite type (SFTs) in dimension d > 1. In particular, we prove that the factorization problem is Σ3-complete and the conjugacy problem Σ1-complete in the arithmetical hierarchy.
متن کاملHardness of Conjugacy, Embedding and Factorization of multidimensional Subshifts of Finite Type
Subshifts of finite type are sets of colorings of the plane defined by local constraints. They can be seen as a discretization of continuous dynamical systems. We investigate here the hardness of deciding factorization, conjugacy and embedding of subshifts of finite type (SFTs) in dimension d > 1. In particular, we prove that the factorization problem is Σ3-complete and that the conjugacy and e...
متن کامل