{"title":"A stronger Kolmogorov zero-one law for resource-bounded measure","authors":"J. J. Dai","doi":"10.1109/CCC.2001.933887","DOIUrl":null,"url":null,"abstract":"Resource-bounded measure has been defined on the classes E, E/sub 2/, ESPACE, E/sub 2/SPACE, REC, and the class of all languages. It is shown here that if C is any of these classes and X is a set of languages that is closed under finite variations and has outer measure less than 1 in C, then X has measure 0 in C. This result strengthens Lutz's resource-bounded generalization of the classical Kolmogorov zero-one law. It also gives a useful sufficient condition for proving that a set has measure 0 in a complexity class.","PeriodicalId":240268,"journal":{"name":"Proceedings 16th Annual IEEE Conference on Computational Complexity","volume":"16 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2001-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings 16th Annual IEEE Conference on Computational Complexity","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CCC.2001.933887","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
Resource-bounded measure has been defined on the classes E, E/sub 2/, ESPACE, E/sub 2/SPACE, REC, and the class of all languages. It is shown here that if C is any of these classes and X is a set of languages that is closed under finite variations and has outer measure less than 1 in C, then X has measure 0 in C. This result strengthens Lutz's resource-bounded generalization of the classical Kolmogorov zero-one law. It also gives a useful sufficient condition for proving that a set has measure 0 in a complexity class.
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