Loading…
Inclusion problems for patterns with a bounded number of variables
We study the inclusion problems for pattern languages that are generated by patterns with a bounded number of variables. This continues the work by Freydenberger and Reidenbach [D.D. Freydenberger, D. Reidenbach, Bad news on decision problems for patterns, Information and Computation 208 (1) (2010)...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Default Article |
| Published: |
2012
|
| Subjects: | |
| Online Access: | https://hdl.handle.net/2134/26545 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1823269247258722304 |
|---|---|
| author | Joachim Bremer Dominik Freydenberger |
| author_facet | Joachim Bremer Dominik Freydenberger |
| author_sort | Joachim Bremer (7168247) |
| collection | Figshare |
| description | We study the inclusion problems for pattern languages that are generated by patterns with a bounded number of variables. This continues the work by Freydenberger and Reidenbach [D.D. Freydenberger, D. Reidenbach, Bad news on decision problems for patterns, Information and Computation 208 (1) (2010) 83-96] by showing that restricting the inclusion problem to significantly more restricted classes of patterns preserves undecidability, at least for comparatively large bounds. For smaller bounds, we prove the existence of classes of patterns with complicated inclusion relations, and an open inclusion problem, that are related to the Collatz Conjecture. In addition to this, we give the first proof of the undecidability of the inclusion problem for NE-pattern languages that, in contrast to previous proofs, does not rely on the inclusion problem for E-pattern languages, and proves the undecidability of the inclusion problem for NE-pattern languages over binary and ternary alphabets. © 2012 Elsevier Inc. |
| format | Default Article |
| id | rr-article-9401522 |
| institution | Loughborough University |
| publishDate | 2012 |
| record_format | Figshare |
| spelling | rr-article-94015222012-01-01T00:00:00Z Inclusion problems for patterns with a bounded number of variables Joachim Bremer (7168247) Dominik Freydenberger (3718891) Other information and computing sciences not elsewhere classified untagged Information and Computing Sciences not elsewhere classified We study the inclusion problems for pattern languages that are generated by patterns with a bounded number of variables. This continues the work by Freydenberger and Reidenbach [D.D. Freydenberger, D. Reidenbach, Bad news on decision problems for patterns, Information and Computation 208 (1) (2010) 83-96] by showing that restricting the inclusion problem to significantly more restricted classes of patterns preserves undecidability, at least for comparatively large bounds. For smaller bounds, we prove the existence of classes of patterns with complicated inclusion relations, and an open inclusion problem, that are related to the Collatz Conjecture. In addition to this, we give the first proof of the undecidability of the inclusion problem for NE-pattern languages that, in contrast to previous proofs, does not rely on the inclusion problem for E-pattern languages, and proves the undecidability of the inclusion problem for NE-pattern languages over binary and ternary alphabets. © 2012 Elsevier Inc. 2012-01-01T00:00:00Z Text Journal contribution 2134/26545 https://figshare.com/articles/journal_contribution/Inclusion_problems_for_patterns_with_a_bounded_number_of_variables/9401522 CC BY-NC-ND 4.0 |
| spellingShingle | Other information and computing sciences not elsewhere classified untagged Information and Computing Sciences not elsewhere classified Joachim Bremer Dominik Freydenberger Inclusion problems for patterns with a bounded number of variables |
| title | Inclusion problems for patterns with a bounded number of variables |
| title_full | Inclusion problems for patterns with a bounded number of variables |
| title_fullStr | Inclusion problems for patterns with a bounded number of variables |
| title_full_unstemmed | Inclusion problems for patterns with a bounded number of variables |
| title_short | Inclusion problems for patterns with a bounded number of variables |
| title_sort | inclusion problems for patterns with a bounded number of variables |
| topic | Other information and computing sciences not elsewhere classified untagged Information and Computing Sciences not elsewhere classified |
| url | https://hdl.handle.net/2134/26545 |