{"title":"分离为点深度二","authors":"Thomas Place, M. Zeitoun","doi":"10.46298/lmcs-17(3:24)2021","DOIUrl":null,"url":null,"abstract":"The dot-depth hierarchy of Brzozowski and Cohen is a classification of all first-order definable languages. It rose to prominence following the work of Thomas, who established an exact correspondence with the quantifier alternation hierarchy of first-order logic: each level contains languages that can be defined with a prescribed number of quantifier blocks. One of the most famous open problems in automata theory is to obtain membership algorithms for all levels in this hierarchy.","PeriodicalId":313950,"journal":{"name":"2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"141 2 Suppl 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2017-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"24","resultStr":"{\"title\":\"Separation for dot-depth two\",\"authors\":\"Thomas Place, M. Zeitoun\",\"doi\":\"10.46298/lmcs-17(3:24)2021\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The dot-depth hierarchy of Brzozowski and Cohen is a classification of all first-order definable languages. It rose to prominence following the work of Thomas, who established an exact correspondence with the quantifier alternation hierarchy of first-order logic: each level contains languages that can be defined with a prescribed number of quantifier blocks. One of the most famous open problems in automata theory is to obtain membership algorithms for all levels in this hierarchy.\",\"PeriodicalId\":313950,\"journal\":{\"name\":\"2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)\",\"volume\":\"141 2 Suppl 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-06-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"24\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.46298/lmcs-17(3:24)2021\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46298/lmcs-17(3:24)2021","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The dot-depth hierarchy of Brzozowski and Cohen is a classification of all first-order definable languages. It rose to prominence following the work of Thomas, who established an exact correspondence with the quantifier alternation hierarchy of first-order logic: each level contains languages that can be defined with a prescribed number of quantifier blocks. One of the most famous open problems in automata theory is to obtain membership algorithms for all levels in this hierarchy.
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