{"title":"On the power of local graph expansion grammars with and without additional restrictions","authors":"","doi":"10.1016/j.tcs.2024.114763","DOIUrl":null,"url":null,"abstract":"<div><p>We study graph expansion grammars, a type of graph grammar that has recently been introduced with motivations in natural language processing. Graph expansion generalizes the well-known hyperedge replacement. In contrast to the latter, the former is able to generate graph languages of unbounded treewidth, like the set of all graphs. In an earlier paper, the complexity of the membership problem of the generated languages was studied, the main result being a polynomial parsing algorithm for local DAG expansion grammars (there called local DAG expansion grammars), a subclass of graph expansion grammars that generates directed acyclic graphs. Here, we study the generative power of local graph expansion grammars. While they, unrestricted, are able to simulate Turing machines, we identify natural restrictions that give rise to a pumping lemma and ensure that the generated languages have regular path languages as well as a semi-linear Parikh image.</p></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0304397524003803/pdfft?md5=4d87e5d2112df783f3aececeec885525&pid=1-s2.0-S0304397524003803-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical Computer Science","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0304397524003803","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
We study graph expansion grammars, a type of graph grammar that has recently been introduced with motivations in natural language processing. Graph expansion generalizes the well-known hyperedge replacement. In contrast to the latter, the former is able to generate graph languages of unbounded treewidth, like the set of all graphs. In an earlier paper, the complexity of the membership problem of the generated languages was studied, the main result being a polynomial parsing algorithm for local DAG expansion grammars (there called local DAG expansion grammars), a subclass of graph expansion grammars that generates directed acyclic graphs. Here, we study the generative power of local graph expansion grammars. While they, unrestricted, are able to simulate Turing machines, we identify natural restrictions that give rise to a pumping lemma and ensure that the generated languages have regular path languages as well as a semi-linear Parikh image.
我们研究的是图扩展语法,它是最近在自然语言处理领域推出的一种图语法。图扩展语法概括了著名的超edge 替换法。与后者不同的是,前者能够生成无界树宽的图语言,比如所有图的集合。在早先的一篇论文中,我们研究了生成语言的成员问题的复杂性,主要成果是局部 DAG 扩展语法(此处称为局部 DAG 扩展语法)的多项式解析算法,这是一种生成有向无环图的图扩展语法子类。在这里,我们研究了局部图扩展语法的生成能力。虽然它们在不受限制的情况下能够模拟图灵机,但我们找出了能产生抽水稃法的自然限制,并确保生成的语言具有规则路径语言以及半线性帕里克图像。
期刊介绍:
Theoretical Computer Science is mathematical and abstract in spirit, but it derives its motivation from practical and everyday computation. Its aim is to understand the nature of computation and, as a consequence of this understanding, provide more efficient methodologies. All papers introducing or studying mathematical, logic and formal concepts and methods are welcome, provided that their motivation is clearly drawn from the field of computing.