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How to Demonstrate Metalinearness and Regularity by Tree-Restricted General Grammars

Formal Languages and Automata Theory 2024-09-12 v1

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

R2 v1 2026-06-28T18:40:39.866Z