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

arXiv - CS - Formal Languages and Automata Theory Pub Date : 2024-09-11 DOI:arxiv-2409.06972

Martin HavelBrno University of Technology, Faculty of Information Technology, Zbyněk KřivkaBrno University of Technology, Faculty of Information Technology, Alexander MedunaBrno University of Technology, Faculty of Information Technology

{"title":"How to Demonstrate Metalinearness and Regularity by Tree-Restricted General Grammars","authors":"Martin HavelBrno University of Technology, Faculty of Information Technology, Zbyněk KřivkaBrno University of Technology, Faculty of Information Technology, Alexander MedunaBrno University of Technology, Faculty of Information Technology","doi":"arxiv-2409.06972","DOIUrl":null,"url":null,"abstract":"This paper introduces derivation trees for general grammars. Within these\ntrees, it defines context-dependent pairs of nodes, corresponding to rewriting\ntwo neighboring symbols using a non context-free rule. It proves that the\nlanguage generated by a linear core general grammar with a slow-branching\nderivation tree is k-linear if there is a constant u such that every sentence w\nin the generated language is the frontier of a derivation tree in which any\npair of neighboring paths contains u or fewer context-dependent pairs of nodes.\nNext, it proves that the language generated by a general grammar with a regular\ncore is regular if there is a constant u such that every sentence w in the\ngenerated language is the frontier of a derivation tree in which any pair of\nneighboring paths contains u or fewer context-dependent pairs of nodes. The\npaper explains that this result is a powerful tool for showing that certain\nlanguages are k-linear or regular.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"s1-8 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - CS - Formal Languages and Automata Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.06972","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

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.

查看原文本刊更多论文

如何通过树状限制的通用语法证明金属线性和规则性

本文介绍了一般语法的推导树。在推导树中，它定义了与上下文相关的节点对，对应于使用非无上下文规则重写两个相邻符号。如果存在一个常数 u，使得生成语言中的每个句子都是派生树的前沿，在派生树中，任何一对相邻路径都包含 u 或更少的上下文相关节点对，那么它就证明了具有慢分支派生树的线性核心通用语法生成的语言是 k 线性的。接下来，论文证明，如果存在一个常数 u，使得生成语言中的每个句子 w 都是一棵派生树的前沿，在这棵派生树中，任何一对相邻路径都包含 u 或更少的上下文相关节点对，那么由具有正则核的一般语法生成的语言就是正则语言。论文解释说，这一结果是证明某些语言是 k 线性或正则性语言的有力工具。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

arXiv - CS - Formal Languages and Automata Theory

自引率

0.00%

发文量