{"title":"Clump Combinatorics, Automata, and Word Asymptotics","authors":"M. Régnier, Billy Fang, Daria Iakovishina","doi":"10.1137/1.9781611973204.6","DOIUrl":null,"url":null,"abstract":"Given a set of words and a probability model for random texts, we are interested in the behavior of occurrences of the words in a random text. Clumps are shown here to play a central role in these problems. They can be used to calculate relevant quantities, such as the probability that a random text contains a given number of pattern word occurrences. We provide combinatorial properties that greatly simplify the classical enumeration of these texts by inclusion-exclusion approaches. We describe two clump automata that can be used to efficiently calculate generating functions.","PeriodicalId":340112,"journal":{"name":"Workshop on Analytic Algorithmics and Combinatorics","volume":"4 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2014-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Workshop on Analytic Algorithmics and Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1137/1.9781611973204.6","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
Abstract
Given a set of words and a probability model for random texts, we are interested in the behavior of occurrences of the words in a random text. Clumps are shown here to play a central role in these problems. They can be used to calculate relevant quantities, such as the probability that a random text contains a given number of pattern word occurrences. We provide combinatorial properties that greatly simplify the classical enumeration of these texts by inclusion-exclusion approaches. We describe two clump automata that can be used to efficiently calculate generating functions.
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