{"title":"关于一阶树可定义集测度的计算","authors":"Marcin Przybylko","doi":"10.4204/EPTCS.277.15","DOIUrl":null,"url":null,"abstract":"We consider the problem of computing the measure of a regular language of infinite binary trees. While the general case remains unsolved, we show that the measure of a language defined by a first-order formula with no descendant relation or by a Boolean combination of conjunctive queries (with descendant relation) is rational and computable. Additionally, we provide an example of a first-order formula that uses descendant relation and defines a language of infinite trees having an irrational measure.","PeriodicalId":10720,"journal":{"name":"CoRR","volume":"8 1","pages":"206-219"},"PeriodicalIF":0.0000,"publicationDate":"2018-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"On Computing the Measures of First-Order Definable Sets of Trees\",\"authors\":\"Marcin Przybylko\",\"doi\":\"10.4204/EPTCS.277.15\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider the problem of computing the measure of a regular language of infinite binary trees. While the general case remains unsolved, we show that the measure of a language defined by a first-order formula with no descendant relation or by a Boolean combination of conjunctive queries (with descendant relation) is rational and computable. Additionally, we provide an example of a first-order formula that uses descendant relation and defines a language of infinite trees having an irrational measure.\",\"PeriodicalId\":10720,\"journal\":{\"name\":\"CoRR\",\"volume\":\"8 1\",\"pages\":\"206-219\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-09-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"CoRR\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4204/EPTCS.277.15\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"CoRR","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4204/EPTCS.277.15","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On Computing the Measures of First-Order Definable Sets of Trees
We consider the problem of computing the measure of a regular language of infinite binary trees. While the general case remains unsolved, we show that the measure of a language defined by a first-order formula with no descendant relation or by a Boolean combination of conjunctive queries (with descendant relation) is rational and computable. Additionally, we provide an example of a first-order formula that uses descendant relation and defines a language of infinite trees having an irrational measure.