How to Demonstrate Metalinearness and Regularity by Tree-Restricted General Grammars
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914947195207680 |
|---|---|
| author | Havel, Martin Křivka, Zbyněk Meduna, Alexander |
| author_facet | Havel, Martin Křivka, Zbyněk Meduna, Alexander |
| contents | This paper introduces derivation trees for general grammars. Within these trees, it defines context-dependent pairs of nodes, corresponding to rewriting two neighboring symbols using a non context-free rule. It proves that the language generated by a linear core general grammar with a slow-branching derivation tree is k-linear if there is a constant u such that every sentence w in the generated language is the frontier of a derivation tree in which any pair of neighboring paths contains u or fewer context-dependent pairs of nodes. Next, it proves that the language generated by a general grammar with a regular core is regular if there is a constant u such that every sentence w in the generated language is the frontier of a derivation tree in which any pair of neighboring paths contains u or fewer context-dependent pairs of nodes. The paper explains that this result is a powerful tool for showing that certain languages are k-linear or regular. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06972 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | How to Demonstrate Metalinearness and Regularity by Tree-Restricted General Grammars Havel, Martin Křivka, Zbyněk Meduna, Alexander Formal Languages and Automata Theory F.4.3 This paper introduces derivation trees for general grammars. Within these trees, it defines context-dependent pairs of nodes, corresponding to rewriting two neighboring symbols using a non context-free rule. It proves that the language generated by a linear core general grammar with a slow-branching derivation tree is k-linear if there is a constant u such that every sentence w in the generated language is the frontier of a derivation tree in which any pair of neighboring paths contains u or fewer context-dependent pairs of nodes. Next, it proves that the language generated by a general grammar with a regular core is regular if there is a constant u such that every sentence w in the generated language is the frontier of a derivation tree in which any pair of neighboring paths contains u or fewer context-dependent pairs of nodes. The paper explains that this result is a powerful tool for showing that certain languages are k-linear or regular. |
| title | How to Demonstrate Metalinearness and Regularity by Tree-Restricted General Grammars |
| topic | Formal Languages and Automata Theory F.4.3 |
| url | https://arxiv.org/abs/2409.06972 |