{"title":"布尔函数上的生长树分布","authors":"B. Chauvin, Danièle Gardy, Cécile Mailler","doi":"10.1137/1.9781611973013.5","DOIUrl":null,"url":null,"abstract":"We define a probability distribution over the set of Boolean functions of k variables induced by the tree representation of Boolean expressions. The law we are interested in is inspired by the growth model of Binary Search Trees: we call it the growing tree law. We study it over different logical systems and compare the results we obtain to already known distributions induced by the tree representation: Catalan trees, Galton-Watson trees and balanced trees.","PeriodicalId":340112,"journal":{"name":"Workshop on Analytic Algorithmics and Combinatorics","volume":"5 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2011-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"The Growing Trees Distribution on Boolean Functions\",\"authors\":\"B. Chauvin, Danièle Gardy, Cécile Mailler\",\"doi\":\"10.1137/1.9781611973013.5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We define a probability distribution over the set of Boolean functions of k variables induced by the tree representation of Boolean expressions. The law we are interested in is inspired by the growth model of Binary Search Trees: we call it the growing tree law. We study it over different logical systems and compare the results we obtain to already known distributions induced by the tree representation: Catalan trees, Galton-Watson trees and balanced trees.\",\"PeriodicalId\":340112,\"journal\":{\"name\":\"Workshop on Analytic Algorithmics and Combinatorics\",\"volume\":\"5 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2011-01-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Workshop on Analytic Algorithmics and Combinatorics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1137/1.9781611973013.5\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Workshop on Analytic Algorithmics and Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1137/1.9781611973013.5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The Growing Trees Distribution on Boolean Functions
We define a probability distribution over the set of Boolean functions of k variables induced by the tree representation of Boolean expressions. The law we are interested in is inspired by the growth model of Binary Search Trees: we call it the growing tree law. We study it over different logical systems and compare the results we obtain to already known distributions induced by the tree representation: Catalan trees, Galton-Watson trees and balanced trees.
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