| Publication type: |
 |
Preprint, Working Paper, ... |
|
| Subject: |
|
Computer Science/Discrete Mathematics
|
|
| Title: |
|
Turing degrees of multidimensional SFTs |
|
| Author(s): |
|
Emmanuel Jeandel ( ) 1, Pascal Vanier () 1 |
|
| Laboratory: |
|
|
|
| Abstract: |
|
In this paper we are interested in computability aspects of subshifts and in particular Turing degrees of 2-dimensional SFTs (i.e. tilings). To be more precise, we prove that given any \pizu subset $P$ of $\{0,1\}^\NN$ there is a SFT $X$ such that $P\times\ZZ^2$ is recursively homeomorphic to $X\setminus U$ where $U$ is a computable set of points. As a consequence, if $P$ contains a recursive member, $P$ and $X$ have the exact same set of Turing degrees. On the other hand, we prove that if $X$ contains only non-recursive members, some of its members always have different but comparable degrees. This gives a fairly complete study of Turing degrees of SFTs. |
|
| Fulltext language: |
|
English |
|
|
| Keyword(s): |
|
Tilings – Subshift of Finite Type – Undecidability – \pizu classes – Turing degree |
|
|
Export this paper
