How to Demonstrate Metalinearness and Regularity by Tree-Restricted General Grammars
Abstract
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.
Keywords
Cite
@article{arxiv.2409.06972,
title = {How to Demonstrate Metalinearness and Regularity by Tree-Restricted General Grammars},
author = {Martin Havel and Zbyněk Křivka and Alexander Meduna},
journal= {arXiv preprint arXiv:2409.06972},
year = {2024}
}
Comments
In Proceedings NCMA 2024, arXiv:2409.06120