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arXiv · 2409.06972

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

Martin Havel·Zbyněk Křivka·Alexander Meduna
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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.

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Martin Havel, Zbyněk Křivka, Alexander Meduna. 2024-09-11. How to Demonstrate Metalinearness and Regularity by Tree-Restricted General Grammars. https://doi.org/10.4204/eptcs.407.7

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