An introduction to symbolic dynamics and coding
An introduction to symbolic dynamics and coding
An aperiodic set of 13 Wang tiles
Discrete Mathematics
A small aperiodic set of Wang tiles
Discrete Mathematics
Theoretical Computer Science
Computability of Countable Subshifts in One Dimension
Theory of Computing Systems - CiE: Programs, Proofs, Processes
| Hi-index | 5.23 |
In this paper, we are interested in computability aspects of subshifts and in particular Turing degrees of two-dimensional subshifts of finite type (SFTs) (i.e., tilings). To be more precise, we prove that, given any @P"1^0 class P of {0,1}^N, there is an SFT X such that PxZ^2 is recursively homeomorphic to X@?U, where U is a computable set of points. As a consequence, if P contains a computable member, P and X have the exact same set of Turing degrees. On the other hand, we prove that, if X contains only non-computable members, some of its members always have different but comparable degrees. This gives a fairly complete study of Turing degrees of SFTs.