{"title":"关于一阶可定义树状语言的一些评论","authors":"Achim Blumensath","doi":"arxiv-2407.01169","DOIUrl":null,"url":null,"abstract":"We study the question of whether a given regular language of finite trees can\nbe defined in first-order logic. We develop an algebraic approach to address\nthis question and we use it to derive several necessary and sufficient\nconditions for definability (but unfortunately no condition that is both). The\nmain difference of our results to those from the literature is that our\nconditions are decidable.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"29 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some Remarks on First-Order Definable Tree Languages\",\"authors\":\"Achim Blumensath\",\"doi\":\"arxiv-2407.01169\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the question of whether a given regular language of finite trees can\\nbe defined in first-order logic. We develop an algebraic approach to address\\nthis question and we use it to derive several necessary and sufficient\\nconditions for definability (but unfortunately no condition that is both). The\\nmain difference of our results to those from the literature is that our\\nconditions are decidable.\",\"PeriodicalId\":501124,\"journal\":{\"name\":\"arXiv - CS - Formal Languages and Automata Theory\",\"volume\":\"29 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-01\",\"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-2407.01169\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - CS - Formal Languages and Automata Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.01169","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Some Remarks on First-Order Definable Tree Languages
We study the question of whether a given regular language of finite trees can
be defined in first-order logic. We develop an algebraic approach to address
this question and we use it to derive several necessary and sufficient
conditions for definability (but unfortunately no condition that is both). The
main difference of our results to those from the literature is that our
conditions are decidable.
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