On a Rice theorem for dynamical properties of SFTs on groups
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866929761937260544 |
|---|---|
| author | Carrasco-Vargas, Nicanor |
| author_facet | Carrasco-Vargas, Nicanor |
| contents | Let $G$ be a group with undecidable domino problem, such as $\mathbb{Z}^2$. We prove that all nontrivial dynamical properties for sofic $G$-subshifts are undecidable, that this is not true for $G$-SFTs, and an undecidability result for dynamical properties of $G$-SFTs similar to the Adian-Rabin theorem. Furthermore we prove a Rice-like result for dynamical invariants asserting that every computable real-valued invariant for $G$-SFTs that is monotone by disjoint unions and products is constant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_10347 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a Rice theorem for dynamical properties of SFTs on groups Carrasco-Vargas, Nicanor Dynamical Systems Information Theory Combinatorics Group Theory Logic 37B10, 37M99, 03D30, 68Q17 Let $G$ be a group with undecidable domino problem, such as $\mathbb{Z}^2$. We prove that all nontrivial dynamical properties for sofic $G$-subshifts are undecidable, that this is not true for $G$-SFTs, and an undecidability result for dynamical properties of $G$-SFTs similar to the Adian-Rabin theorem. Furthermore we prove a Rice-like result for dynamical invariants asserting that every computable real-valued invariant for $G$-SFTs that is monotone by disjoint unions and products is constant. |
| title | On a Rice theorem for dynamical properties of SFTs on groups |
| topic | Dynamical Systems Information Theory Combinatorics Group Theory Logic 37B10, 37M99, 03D30, 68Q17 |
| url | https://arxiv.org/abs/2401.10347 |