On 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....
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| Format: | Article |
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Open Publishing Association
2012-08-01
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| Series: | Electronic Proceedings in Theoretical Computer Science |
| Online Access: | http://arxiv.org/pdf/1208.2756v1 |
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doaj-f5a51fced0ef46459fa0e52cf2ecdea12020-11-24T23:13:50ZengOpen Publishing AssociationElectronic Proceedings in Theoretical Computer Science2075-21802012-08-0190Proc. AUTOMATA&JAC 2012233610.4204/EPTCS.90.3On Derivatives and Subpattern Orders of Countable SubshiftsVille SaloIlkka TörmäWe 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 of view, a sofic shift whose subpattern poset contains an infinite descending chain, a family of SFTs whose finite subpattern posets contain arbitrary finite posets, and a natural example of an SFT with infinite Cantor-Bendixon rank.http://arxiv.org/pdf/1208.2756v1 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Ville Salo Ilkka Törmä |
| spellingShingle |
Ville Salo Ilkka Törmä On Derivatives and Subpattern Orders of Countable Subshifts Electronic Proceedings in Theoretical Computer Science |
| author_facet |
Ville Salo Ilkka Törmä |
| author_sort |
Ville Salo |
| title |
On Derivatives and Subpattern Orders of Countable Subshifts |
| title_short |
On Derivatives and Subpattern Orders of Countable Subshifts |
| title_full |
On Derivatives and Subpattern Orders of Countable Subshifts |
| title_fullStr |
On Derivatives and Subpattern Orders of Countable Subshifts |
| title_full_unstemmed |
On Derivatives and Subpattern Orders of Countable Subshifts |
| title_sort |
on derivatives and subpattern orders of countable subshifts |
| publisher |
Open Publishing Association |
| series |
Electronic Proceedings in Theoretical Computer Science |
| issn |
2075-2180 |
| publishDate |
2012-08-01 |
| description |
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 of view, a sofic shift whose subpattern poset contains an infinite descending chain, a family of SFTs whose finite subpattern posets contain arbitrary finite posets, and a natural example of an SFT with infinite Cantor-Bendixon rank. |
| url |
http://arxiv.org/pdf/1208.2756v1 |
| work_keys_str_mv |
AT villesalo onderivativesandsubpatternordersofcountablesubshifts AT ilkkatorma onderivativesandsubpatternordersofcountablesubshifts |
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