{"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}
引用次数: 6
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.
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