{"title":"分离词和跟踪重建","authors":"Zachary Chase","doi":"10.1145/3406325.3451118","DOIUrl":null,"url":null,"abstract":"We prove that for any distinct x,y ∈ {0,1}n, there is a deterministic finite automaton with O(n1/3) states that accepts x but not y. This improves Robson’s 1989 bound of O(n2/5). Using a similar complex analytic technique, we improve the upper bound on worst case trace reconstruction, showing that any unknown string x ∈ {0,1}n can be reconstructed with high probability from exp(O(n1/5)) independently generated traces.","PeriodicalId":132752,"journal":{"name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","volume":"14 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"12","resultStr":"{\"title\":\"Separating words and trace reconstruction\",\"authors\":\"Zachary Chase\",\"doi\":\"10.1145/3406325.3451118\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that for any distinct x,y ∈ {0,1}n, there is a deterministic finite automaton with O(n1/3) states that accepts x but not y. This improves Robson’s 1989 bound of O(n2/5). Using a similar complex analytic technique, we improve the upper bound on worst case trace reconstruction, showing that any unknown string x ∈ {0,1}n can be reconstructed with high probability from exp(O(n1/5)) independently generated traces.\",\"PeriodicalId\":132752,\"journal\":{\"name\":\"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing\",\"volume\":\"14 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-06-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"12\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/3406325.3451118\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3406325.3451118","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We prove that for any distinct x,y ∈ {0,1}n, there is a deterministic finite automaton with O(n1/3) states that accepts x but not y. This improves Robson’s 1989 bound of O(n2/5). Using a similar complex analytic technique, we improve the upper bound on worst case trace reconstruction, showing that any unknown string x ∈ {0,1}n can be reconstructed with high probability from exp(O(n1/5)) independently generated traces.
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