{"title":"聚类组合、自动机和词渐近","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":"{\"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}","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}
Clump Combinatorics, Automata, and Word Asymptotics
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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